Source Code

These source-code files were derived from scans of the Colossus 237 (Apollo 8 Command Module) program listing from the private collection of original AGC developer Fred Martin. Scanning was by Ron Burkey. Pre-existing Colossus 249 (Apollo 9 CM) source files were used as a template, and changes between Colossus 249 and Colossus 237 were manually transcribed by a team of volunteers. Note that the page images presented online are of reduced quality, and that additional images are available. Report any conversion errors or legibility problems in page images to info@sandroid.org. Notations on the program listing read, in part:

	GAP: ASSEMBLE REVISION 237 OF AGC PROGRAM COLOSSUS 
	BY NASA 2021111-031  1:17 AUG. 24, 1968
Note that the date is the date of the printout, not the date of the program revision.

046544,000002:                                                                                                  ## Copyright:   Public domain.
046545,000003:                                                                                                  ## Filename:    INTERPRETER.agc
046546,000004:                                                                                                  ## Purpose:     Part of the source code for Colossus build 237.
046547,000005:                                                                                                  ##              This is for the Command Module's (CM) Apollo Guidance
046548,000006:                                                                                                  ##              Computer (AGC), for Apollo 8.
046549,000007:                                                                                                  ## Assembler:   yaYUL
046550,000008:                                                                                                  ## Contact:     Jim Lawton <jim DOT lawton AT gmail DOT com>
046551,000009:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
046552,000010:                                                                                                  ## Page Scans:  www.ibiblio.org/apollo/ScansForConversion/Colossus237/
046553,000011:                                                                                                  ## Mod history: 2011-04-09 JL   Adapted from corresponding Colossus 249 file.
046554,000012:                                                                                                  ##              2016-11-02 RSB  Typo (offset-reference -1 was not indented).
046555,000013:                                                                                                  ##              2017-01-01 RSB  Proofed comment text using octopus/ProoferComments,
046556,000014:                                                                                                  ##                              and fixed errors found.
046557,000015:                                                                                                  ##              2017-01-14 RSB  Fixed comment-text errors located whilst diff'ing
046558,000016:                                                                                                  ##                              against Colossus 249.
046559,000017:                                                                                                  ##              2017-02-05 RSB  Back-ported comment corrections 
046560,000018:                                                                                                  ##                              identified while proofing Artemis 072.
046561,000019:                                                                                                  ##              2017-03-15 RSB  Comment-text fixes identified in 5-way
046562,000020:                                                                                                  ##                              side-by-side diff of Luminary 69/99/116/131/210.
046563,000021: 

Page 1074

046565,000023:                                                                                                  #  SECTION 1  DISPATCHER
046566,000024: 
046567,000025:                                                                                                  #           ENTRY TO THE INTERPRETER. INTPRET SETS LOC TO THE FIRST  INSTRUCTION, BANKSET TO THE BBANK OF THE
046568,000026:                                                                                                  #  OBJECT INTERPRETIVE PROGRAM, AND INTBIT15 TO THE BIT15 CONTENTS OF FBANK. INTERPRETIVE PROGRAMS MAY BE IN
046569,000027:                                                                                                  #  VIRTUALLY ALL BANKS PRESENT UNDER ANY SUPER-BANK SETTING, WITH THE RESTRICTION THAT PROGRAMS IN HIGH BANKS
046570,000028:                                                                                                  #  (BIT15 OF FBANK = 1) DO NOT REFER TO LOWBANKS, AND VICE-VERSA. THE INTERPRETER DOES NOT SWITCH SUPERBANKS.
046571,000029:                                                                                                  #  E-BANK SWITCHING OCCURS WHENEVER GENERAL ERASABLE (100 - 3777) IS ADDRESSED.
046572,000030: 
046573,000031: 
046574,000032:    6006                                           BLOCK    03                                    
046575,000033: 
046576,000034:    6006                                           COUNT    03/INTER                              
046577,000035: 
046578,000036:    6006           00003        INTPRET            RELINT                                         
046579,000037:    6007           00006                           EXTEND                                         #  SET LOC TO THE WORD FOLLOWING THE TC.
046580,000038:    6010           22164                           QXCH     LOC                                   
046581,000039: 
046582,000040:    6011           30006                 +2        CA       BBANK                                 #  INTERPRETIVE BRANCHES FINISH HERE.
046583,000041:    6012           54165                           TS       BANKSET                               
046584,000042:    6013           74674                           MASK     BIT15                                 #  GET 15TH BIT FOR INDEXABLE ADDRESSES.
046585,000043:    6014           54115                           TS       INTBIT15                              
046586,000044: 
046587,000045:    6015           54023                           TS       EDOP                                  #  MAKE SURE NO INSTRUCTIONS LEFT OVER
046588,000046: 
046589,000047:    6016           16037                           TCF      NEWOPS                                #  PICK UP OP CODE PAIR AND BEGIN.
046590,000048: 
046591,000049: 
046592,000050:    6017           22006        INTRSM             LXCH     BBANK                                 #  RESUME SUSPENDED INTERPRETIVE JOB
046593,000051:    6020           16011                           TCF      INTPRET    +3                         
046594,000052:                                                                                                  #           DLOAD LOADS MPAC, MPAC +1, LEAVING ZERO IN MPAC +2.
046595,000053: 
046596,000054:    6021           00006        DLOAD              EXTEND                                         
046597,000055:    6022           50116                           INDEX    ADDRWD                                
046598,000056:    6023           30001                           DCA      0                                     #  LOAD DP C(C(ADDRWD)) INTO MPAC,MPAX +1
046599,000057:    6024           52155        SLOAD2             DXCH     MPAC                                  
046600,000058:    6025           34714                           CAF      ZERO                                  #  ZERO MPAC +2
046601,000059: 

Page 1075

046603,000061:                                                                                                  #           AT THE END OF MOST INSTRUCTIONS, CONTROL IS GIVEN TO DANZIG TO DISPATCH THE NEXT OPERATION.
046604,000062: 
046605,000063:    6026           54156                           TS       MPAC       +2                         #  AND DECLARE DP MODE
046606,000064: 
046607,000065:    6027           54163        NEWMODE            TS       MODE                                  #  PROLOGUE FOR MODE-CHANGING INSTRUCTIONS.
046608,000066: 
046609,000067:    6030           30165        DANZIG             CA       BANKSET                               #  SET BBANK BEFORE TESTING NEWJOB SO THAT
046610,000068:    6031           54006                           TS       BBANK                                 #  IT MAY BE SAVED DIRECTLY BY CHANJOB.
046611,000069: 
046612,000070:    6032           10023        NOIBNKSW           CCS      EDOP                                  #  SEE IF AN ORDER CODE IS LEFT OVER FROM
046613,000071:    6033           16046                           TCF      OPJUMP                                #  THE LAST PAIR RETRIEVED. IF SO, EXECUTE.
046614,000072:                                                                                                  #                                          EDOP IS SET TO ZERO ON ITS RE-EDITING.
046615,000073: 
046616,000074:    6034           10067                           CCS      NEWJOB                                #  SEE IF A JOB OF HIGHER PRIORITY IS
046617,000075:    6035           15063                           TCF      CHANG2                                #  PRESENT, AND IF SO, CHANGE JOBS.
046618,000076: 
046619,000077:    6036           24164                           INCR     LOC                                   #  ADVANCE THE LOCATION COUNTER.
046620,000078:                                                                                                  #           ITRACE (1) REFERS TO "NEWOPS".
046621,000079:    6037           50164        NEWOPS             INDEX    LOC                                   #  ENTRY TO BEGIN BY PICKING OP CODE PAIR.
046622,000080:    6040           30000                           CA       0                                     #  MAY BE AN OPCODE PAIR OR A STORE CODE.
046623,000081:    6041           10000                           CCS      A                                     #  TEST SIGN AND GET DABS(A).
046624,000082:    6042           16331                           TCF      DOSTORE                               #  PROCESS STORE CODE.
046625,000083: 
046626,000084:    6043           00177        LOW7               OCT      177                                   
046627,000085: 
046628,000086:    6044           54023                           TS       EDOP                                  #  OP CODE PAIR. LEAVE THE OTHER IN EDOP
046629,000087:    6045           76043                           MASK     LOW7                                  #  WHERE CCS EDOP WILL HONOR IT NEXT.
046630,000088: 
046631,000089:    6046           54020        OPJUMP             TS       CYR                                   #  LOWWD ENTERS HERE IF A RIGHT-HAND OP
046632,000090:    6047           10020                           CCS      CYR                                   #  CODE IS TO BE PROCESSED. TEST PREFICES.
046633,000091:    6050           16216                           TCF      OPJUMP2                               #  TEST SECOND PREFIX BIT.
046634,000092: 
046635,000093:    6051           16712                           TCF      EXIT                                  #  +0 OP CODE IS EXIT.
046636,000094: 

Page 1076

046638,000096:                                                                                                  #           PROCESS ADDRESSES WHICH MAY BE DIRECT, INDEXED, OR REFERENCE THE PUSHDOWN LIST.
046639,000097: 
046640,000098:    6052           74712        ADDRESS            MASK     BIT1                                  #  SEE IF ADDRESS IS INDEXED. CYR CONTAINED
046641,000099:    6053           10000                           CCS      A                                     #  400XX, SO BIT 1 IS NOW AS IT WAS IN CYR.
046642,000100:    6054           16115                           TCF      INDEX                                 #  FORM INDEXED ADDRESS.
046643,000101: 
046644,000102:    6055           50164        DIRADRES           INDEX    LOC                                   #  LOOK AHEAD TO NEXT WORD TO SEE IF
046645,000103:    6056           40001        OCT40001           CS       1                                     #  ADDRESS IS GIVEN.
046646,000104:    6057           10000                           CCS      A                                     
046647,000105:    6060           16164                           TCF      PUSHUP                                #  IF NOT.
046648,000106: 
046649,000107:    6061           77773        NEG4               DEC      -4         B-14                       
046650,000108: 
046651,000109:    6062           24164                           INCR     LOC                                   #  IF SO, TO SHOW WE PICKED UP A WORD.
046652,000110:    6063           54116                           TS       ADDRWD                                
046653,000111: 

Page 1077

046655,000113:                                                                                                  #           FINAL DIGESTION OF DIRECT ADDRESSES OF OP CODES WITH 01 PREFIX IS DONE HERE. IN EACH CASE, THE
046656,000114:                                                                                                  #  REQUIRED 12-BIT SUB-ADDRESS IS LEFT IN ADDRWD, WITH ANY REQUIRED E OR F BANK SWITCHING DONE. ADDRESSES LESS
046657,000115:                                                                                                  #  THAN 45D ARE TAKEN TO BE RELATIVE TO THE WORK AREA. THE OP CODE IS NOW IN BITS 1-5 OF CYR WITH BIT 14 = 1.
046658,000116: 
046659,000117: 
046660,000118:    6064           66220                           AD       -ENDVAC                               #  SEE IF ADDRESS RELATIVE TO WORK AREA.
046661,000119:    6065           10000                           CCS      A                                     
046662,000120:    6066           67712                           AD       -ENDERAS                              #  IF NOT, SEE IF IN GENERAL ERASABLE.
046663,000121:    6067           16074                           TCF      IERASTST                              
046664,000122: 
046665,000123:    6070           30120        NETZERO            CA       FIXLOC                                #  IF SO, LEAVE THE MODIFIED ADDRESS IN
046666,000124:    6071           26116                           ADS      ADDRWD                                #  ADDRWD AND DISPATCH.
046667,000125:    6072           50020        ITR15              INDEX    CYR                                   #  THIS INDEX MAKES THE NEXT INSTRUCTION
046668,000126:    6073           76242                           7        INDJUMP    -1                         #  TCF INDJUMP + OP, EDITING CYR.
046669,000127: 
046670,000128:    6074           00006        IERASTST           EXTEND                                         
046671,000129:    6075           66105                           BZMF     GEADDR                                #  GO PROCESS GENERAL-ERASABLE ADDRESS.
046672,000130: 
046673,000131:    6076           74747                           MASK     LOW10                                 #  FIXED BANK ADDRESS. RESTORE AND ADD B15.
046674,000132:    6077           64747                           AD       LOW10                                 #  SWITCH BANKS AND LEAVE SUBADDRESS IN
046675,000133:    6100           56116                           XCH      ADDRWD                                #  ADDRWD FOR OPERAND RETRIEVAL. (THIS
046676,000134:    6101           60115                           AD       INTBIT15                              #  METHOD PRECLUDES USE OF THE LAST
046677,000135:    6102           54004                           TS       FBANK                                 #  LOCATION IN EACH FBANK.)
046678,000136:    6103           50020        ITR12              INDEX    CYR                                   
046679,000137:    6104           76242                           7        INDJUMP    -1                         
046680,000138: 
046681,000139:    6105           74373        GEADDR             MASK     LOW8                                  
046682,000140:    6106           64744                           AD       OCT1400                               
046683,000141:    6107           56116                           XCH      ADDRWD                                
046684,000142:    6110           54003                           TS       EBANK                                 
046685,000143:    6111           50020        ITR10              INDEX    CYR                                   
046686,000144:    6112           76242                           7        INDJUMP    -1                         
046687,000145: 

Page 1078

046689,000147:                                                                                                  #           THE FOLLOWING ROUTINE PROCESSES INTERPRETIVE INDEXED ADDRESSES. AN INTERPRETER INDEX REGISTER MAY
046690,000148:                                                                                                  #  CONTAIN THE ADDRESS OF ANY ERASABLE REGISTER (0-42 BEING RELATIVE TO THE VAC AREA) OR ANY INTERPRETIVE PROGRAM
046691,000149:                                                                                                  #  BANK, OR ANY INTEGER IN THAT RANGE.
046692,000150: 
046693,000151:    6113           37702        DODLOAD*           CAF      DLOAD*                                #  STODL* COMES HERE TO PROCESS LOAD ADR.
046694,000152:    6114           54020                           TS       CYR                                   #  (STOVL* ENTERS HERE).
046695,000153: 
046696,000154:    6115           30120        INDEX              CA       FIXLOC                                #  SET UP INDEX LOCATION.
046697,000155:    6116           54130                           TS       INDEXLOC                              
046698,000156:    6117           24164                           INCR     LOC                                   #  (ADDRESS ALWAYS GIVEN).
046699,000157:    6120           50164                           INDEX    LOC                                   
046700,000158:    6121           40000                           CS       0                                     
046701,000159:    6122           10000                           CCS      A                                     #  INDEX 2 IF ADDRESS STORED COMPLEMENTED.
046702,000160:    6123           24130                           INCR     INDEXLOC                              
046703,000161:    6124           16125                           NOOP                                           
046704,000162: 
046705,000163:    6125           54116                           TS       ADDRWD                                #  14 BIT ADDRESS TO ADDRWD.
046706,000164:    6126           77711                           MASK     HIGH4                                 #  IF ADDRESS GREATER THAN 2K, ADD INTBIT15
046707,000165:    6127           00006                           EXTEND                                         
046708,000166:    6130           16133                           BZF      INDEX2                                
046709,000167:    6131           30115                           CA       INTBIT15                              
046710,000168:    6132           26116                           ADS      ADDRWD                                
046711,000169: 
046712,000170:    6133           50130        INDEX2             INDEX    INDEXLOC                              
046713,000171:    6134           40046                           CS       X1                                    
046714,000172:    6135           26116                           ADS      ADDRWD                                #  DO AUGMENT, IGNORING AND CORRECTING OVF.
046715,000173: 
046716,000174:    6136           77713                           MASK     HIGH9                                 #  SEE IF ADDRESS IS IN WORK AREA.
046717,000175:    6137           00006                           EXTEND                                         
046718,000176:    6140           16153                           BZF      INDWORK                               
046719,000177:    6141           77711                           MASK     HIGH4                                 #  SEE IF IN FIXED BANK.
046720,000178:    6142           00006                           EXTEND                                         
046721,000179:    6143           16155                           BZF      INDERASE                              
046722,000180: 
046723,000181:    6144           30116                           CA       ADDRWD                                #  IN FIXED - SWITCH BANKS AND CREATE
046724,000182:    6145           54004                           TS       FBANK                                 #  SUB-ADDRESS.
046725,000183:    6146           74747                           MASK     LOW10                                 
046726,000184:    6147           64700                           AD       2K                                    
046727,000185:    6150           54116                           TS       ADDRWD                                
046728,000186:    6151           50020        ITR11              INDEX    CYR                                   
046729,000187:    6152           36242                           3        INDJUMP    -1                         
046730,000188: 
046731,000189:    6153           30120        INDWORK            CA       FIXLOC                                #  MAKE ADDRWD RELATIVE TO WORK AREA.
046732,000190:    6154           16161                           TCF      ITR13      -1                         
046733,000191: 
046734,000192:    6155           34744        INDERASE           CA       OCT1400                               
046735,000193:    6156           56116                           XCH      ADDRWD                                
046736,000194:    6157           54003                           TS       EBANK                                 
046737,000195:    6160           74373                           MASK     LOW8                                  
046738,000196:    6161           26116                 -1        ADS      ADDRWD                                

Page 1079

046740,000198:    6162           50020        ITR13              INDEX    CYR                                   
046741,000199:    6163           36242                           3        INDJUMP    -1                         
046742,000200: 

Page 1080

046744,000202:                                                                                                  #           PUSH-UP ROUTINES. WHEN NO OPERAND ADDRESS IS GIVEN, THE APPROPRIATE OPERAND IS TAKEN FROM THE PUSH-DOWN
046745,000203:                                                                                                  #  LIST. IN MOST CASES THE MODE OF THE RESULT (VECTOR OR SCALAR) OF THE LAST ARITHMETIC OPERATION PERFORMED
046746,000204:                                                                                                  #  IS THE SAME AS THE TYPE OF OPERAND DESIRED (ALL ADD/SUBTRACT ETC.). EXCEPTIONS TO THIS GENERAL RULE ARE LISTED
046747,000205:                                                                                                  #  BELOW (NOTE THAT IN EVERY CASE THE MODE REGISTER IS LEFT INTACT):
046748,000206: 
046749,000207:                                                                                                  #           1.  VXSC AND V/SC WANT THE OPPOSITE TYPE OF OPERAND, E.G., IF THE LAST OPERATION YIELDED A VECTOR
046750,000208:                                                                                                  #  RESULT, VXSC WANTS A SCALAR.
046751,000209: 
046752,000210:                                                                                                  #           2.  THE LOAD CODES SHOULD LOAD THE ACCUMULATOR INDEPENDENT OF THE RESULT OF THE LAST OPERATION. THIS
046753,000211:                                                                                                  #  INCLUDES VLOAD, DLOAD, TLOAD, PDDL, AND PDVL (NO PUSHUP WITH SLOAD).
046754,000212: 
046755,000213:                                                                                                  #           3.  SOME ARITHMETIC OPERATIONS REQUIRE A STANDARD TYPE OF OPERAND REGARDLESS OF THE PREVIOUS OPERATION.
046756,000214:                                                                                                  #  THIS INCLUDES SIGN WANTING DP AND TAD REQUIRING TP.
046757,000215: 
046758,000216:    6164           34374        PUSHUP             CAF      OCT23                                 #  IF THE LOW 5 BITS OF CYR ARE LESS THAN
046759,000217:    6165           70020                           MASK     CYR                                   #  20, THIS OP REQUIRES SPECIAL ATTENTION.
046760,000218:    6166           66171                           AD       -OCT10                                #  (NO -0).
046761,000219:    6167           10000                           CCS      A                                     
046762,000220:    6170           16202                           TCF      REGUP                                 #  FOR ALL CODES GREATER THAN OCT 7.
046763,000221: 
046764,000222:    6171           77767        -OCT10             OCT      -10                                   
046765,000223: 
046766,000224:    6172           66061                           AD       NEG4                                  #  WE NOW HAVE 7 - OP CODE(MOD4). SEE IF
046767,000225:    6173           10000                           CCS      A                                     #  THE OP CODE (MOD4) IS THREE (REVERSE).
046768,000226:    6174           50000                           INDEX    A                                     #  NO - THE MODE IS DEFINITE. PICK UP THE
046769,000227:    6175           46213                           CS       NO.WDS                                
046770,000228:    6176           16204                           TCF      REGUP      +2                         
046771,000229: 
046772,000230:    6177           50163                           INDEX    MODE                                  #  FOR VXSC AND V/SC WE WANT THE REQUIRED
046773,000231:    6200           46211                           CS       REVCNT                                #  PUSHLOC DECREMENT WITHOUT CHANGING THE
046774,000232:    6201           16204                           TCF      REGUP      +2                         #  MODE AT THIS TIME.
046775,000233: 
046776,000234:    6202           50163        REGUP              INDEX    MODE                                  #  MOST ALL OP CODES PUSHUP HERE.
046777,000235:    6203           46213                           CS       NO.WDS                                
046778,000236:    6204           26166                 +2        ADS      PUSHLOC                               
046779,000237:    6205           54116                           TS       ADDRWD                                
046780,000238:    6206           50020        ITR14              INDEX    CYR                                   
046781,000239:    6207           76242                           7        INDJUMP    -1                         #  (THE INDEX MAKES THIS A TCF.)
046782,000240: 
046783,000241:    6210           00002                           OCT      2                                     #  REVERSE PUSHUP DECREMENT. VECTOR TAKES 2
046784,000242:    6211           00006        REVCNT             OCT      6                                     #  WORDS, SCALAR TAKES 6.
046785,000243:    6212           00006                           OCT      6                                     
046786,000244:    6213           00002        NO.WDS             OCT      2                                     #  CONVENTIONAL DECREMENT IS 6 WORDS VECTOR
046787,000245:    6214           00003        OCTAL3             OCT      3                                     #  2 IN DP, AND 3 IN TP.
046788,000246:    6215           00006                           OCT      6                                     
046789,000247: 

Page 1081

046791,000249:                                                                                                  #           TEST THE SECOND PREFIX BIT TO SEE IF THIS IS A MISCELLANEOUS OR A UNARY/SHORT SHIFT OPERATION.
046792,000250: 
046793,000251:    6216           10020        OPJUMP2            CCS      CYR                                   #  TEST SECOND PREFIX BIT.
046794,000252:    6217           16232                           TCF      OPJUMP3                               #  TEST THIRD BIT TO SEE IF UNARY OR SHIFT.
046795,000253: 
046796,000254:    6220           77722        -ENDVAC            DEC      -45        B-14                       
046797,000255: 
046798,000256:                                                                                                  #           THE FOLLOWING ROUTINE PROCESSES ADDRESSES OF SUFFIX CLASS 10. THEY ARE BASICALLY WORK AREA ADDRESSES
046799,000257:                                                                                                  #  IN THE RANGE 0 - 52, ERASABLE ECADR CONSTANTS FROM 100 - 3777, AND FCADRS ABOVE THAT. ALL 15 BITS ARE AVAILABLE
046800,000258:                                                                                                  #  IN CONTRAST TO SUFFIX 1, IN WHICH ONLY THE LOW ORDER 14 ARE AVAILABLE.
046801,000259: 
046802,000260:    6221           24164        15BITADR           INCR     LOC                                   #  (ENTRY HERE FROM STCALL).
046803,000261:    6222           50164                           INDEX    LOC                                   #  PICK UP ADDRESS WORD.
046804,000262:    6223           30000                           CA       0                                     
046805,000263:    6224           54117                           TS       POLISH                                #  WE MAY NEED A SUBADDRESS LATER.
046806,000264: 
046807,000265:    6225           34750                           CAF      LOW7+2K                               #  THESE INSTRUCTIONS ARE IN BANK 1.
046808,000266:    6226           54004                           TS       FBANK                                 
046809,000267:    6227           70020                           MASK     CYR                                   
046810,000268:    6230           50000        ITR7               INDEX    A                                     
046811,000269:    6231           16303                           TCF      MISCJUMP                              
046812,000270: 

Page 1082

046814,000272:                                                                                                  #           COMPLETE THE DISPATCHING OF UNARY AND SHORT SHIFT OPERATIONS.
046815,000273: 
046816,000274:    6232           54004        OPJUMP3            TS       FBANK                                 #  CALL IN BANK 0 (BITS 11-15 OF A ARE 0.)
046817,000275:                                                                                                  #           ITRACE (6) REFERS TO "OPJUMP3".
046818,000276:    6233           10020                           CCS      CYR                                   #  TEST THIRD PREFIX BIT.
046819,000277:    6234           50000                           INDEX    A                                     #  THE DECREMENTED UNARY CODE IS IN BITS
046820,000278:    6235           12000                           TCF      UNAJUMP                               #  1-4 OF A (ZERO, EXIT, HAS BEEN DETECTED)
046821,000279: 
046822,000280:    6236           10163                           CCS      MODE                                  #  ITS A SHORT SHIFT CODE. SEE IF PRESENT
046823,000281:    6237           12017                           TCF      SHORTT                                #  SCALAR OR VECTOR.
046824,000282:    6240           12017                           TCF      SHORTT                                
046825,000283:    6241           12121                           TCF      SHORTV                                #  CALLS THE APPROPRIATE ROUTINE.
046826,000284: 
046827,000285: 
046828,000286:    6242     4364               FBANKMSK           EQUALS   BANKMASK                              
046829,000287:    6242           00122        LVBUF              ADRES    VBUF                                  
046830,000288: 

Page 1083

046832,000290:                                                                                                  #           THE FOLLOWING IS THE JUMP TABLE FOR OP CODES WHICH MAY HAVE INDEXABLE ADDRESSES OR MAY PUSH UP.
046833,000291: 
046834,000292:    6243           16454        INDJUMP            TCF      VLOAD                                 #  00 - LOAD MPAC WITH A VECTOR.
046835,000293:    6244           17040                           TCF      TAD                                   #  01 - TRIPLE PRECISION ADD TO MPAC.
046836,000294:    6245           17624                           TCF      SIGN                                  #  02 - COMPLEMENT MPAC (V OR SC) IF X NEG.
046837,000295:    6246           17350                           TCF      VXSC                                  #  03 - VECTOR TIMES SCALAR.
046838,000296:    6247           16652                           TCF      CGOTO                                 #  04 - COMPUTED GO TO.
046839,000297:    6250           16437                           TCF      TLOAD                                 #  05 - LOAD MPAC WITH TRIPLE PRECISION.
046840,000298:    6251           16021                           TCF      DLOAD                                 #  06 - LOAD MPAC WITH A DP SCALAR.
046841,000299:    6252           17573                           TCF      V/SC                                  #  07 - VECTOR DIVIDED BY SCALAR.
046842,000300: 
046843,000301:    6253           16450                           TCF      SLOAD                                 #  10 - LOAD MPAC IN SINGLE PRECISION.
046844,000302:    6254           16567                           TCF      SSP                                   #  11 - SET SINGLE PRECISION INTO X.
046845,000303:    6255           16472                           TCF      PDDL                                  #  12 - PUSH DOWN MPAC AND RE-LOAD IN DP.
046846,000304:    6256           17303                           TCF      MXV                                   #  13 - MATRIX POST-MULTIPLIED BY VECTOR.
046847,000305:    6257           16526                           TCF      PDVL                                  #  14 - PUSH DOWN AND VECTOR LOAD.
046848,000306:    6260           16575                           TCF      CCALL                                 #  15 - COMPUTED CALL.
046849,000307:    6261           17306                           TCF      VXM                                   #  16 - MATRIX PRE-MULTIPLIED BY VECTOR.
046850,000308:    6262           17565                           TCF      TSLC                                  #  17 - NORMALIZE MPAC (SCALAR ONLY).
046851,000309: 
046852,000310:    6263           17543                           TCF      DMPR                                  #  20 - DP MULTIPLY AND ROUND.
046853,000311:    6264           17546                           TCF      DDV                                   #  21 - DP DIVIDE BY.
046854,000312:    6265           17552                           TCF      BDDV                                  #  22 - DP DIVIDE INTO.
046855,000313:    6266           17570                           TCF      GSHIFT                                #  23 - GENERAL SHIFT INSTRUCTION.
046856,000314:    6267           16720                           TCF      VAD                                   #  24 - VECTOR ADD.
046857,000315:    6270           16716                           TCF      VSU                                   #  25 - VECTOR SUBTRACT.
046858,000316:    6271           17005                           TCF      BVSU                                  #  26 - VECTOR SUBTRACT FROM.
046859,000317:    6272           17300                           TCF      DOT                                   #  27 - VECTOR DOT PRODUCT.
046860,000318: 
046861,000319:    6273           17427                           TCF      VXV                                   #  30 - VECTOR CROSS PRODUCT.
046862,000320:    6274           17374                           TCF      VPROJ                                 #  31 - VECTOR PROJECTION.
046863,000321:    6275           16754                           TCF      DSU                                   #  32 - DP SUBTRACT.
046864,000322:    6276           17031                           TCF      BDSU                                  #  33 - DP SUBTRACT FROM.
046865,000323:    6277           16744                           TCF      DAD                                   #  34 - DP ADD.
046866,000324:    6300           16300                           TCF      +0                                    #  35 - AVAILABLE
046867,000325:    6301           17541                           TCF      DMP1                                  #  36 - DP MULTIPLY.
046868,000326:    6302           17562                           TCF      SETPD                                 #  37 - SET PUSH DOWN POINTER (DIRECT ONLY)
046869,000327: 
046870,000328:                                                                                                  #  CODES 10 AND 14 MUST NOT PUSH UP. CODE 04 MAY BE USED FOR VECTOR DECLARE BEFORE PUSHUP IF DESIRED.
046871,000329: 

Page 1084

046873,000331:                                                                                                  #           THE FOLLOWING JUMP TABLE APPLIES TO INDEX, BRANCH, AND MISCELLANEOUS INSTRUCTIONS.
046874,000332: 
046875,000333:    6303           12371        MISCJUMP           TCF      AXT                                   #  00 - ADDRESS TO INDEX TRUE.
046876,000334:    6304           12376                           TCF      AXC                                   #  01 - ADDRESS TO INDEX COMPLEMENTED.
046877,000335:    6305           12401                           TCF      LXA                                   #  02 - LOAD INDEX FROM ERASABLE.
046878,000336:    6306           12405                           TCF      LXC                                   #  03 - LOAD INDEX FROM COMPLEMENT OF ERAS.
046879,000337:    6307           12411                           TCF      SXA                                   #  04 - STORE INDEX IN ERASABLE.
046880,000338:    6310           12417                           TCF      XCHX                                  #  05 - EXCHANGE INDEX WITH ERASABLE.
046881,000339:    6311           12433                           TCF      INCR                                  #  06 - INCREMENT INDEX REGISTER.
046882,000340:    6312           12442                           TCF      TIX                                   #  07 - TRANSFER ON INDEX.
046883,000341: 
046884,000342:    6313           12425                           TCF      XAD                                   #  10 - INDEX REGISTER ADD FROM ERASABLE.
046885,000343:    6314           12436                           TCF      XSU                                   #  11 - INDEX SUBTRACT FROM ERASABLE.
046886,000344:    6315           12514                           TCF      BZE/GOTO                              #  12 - BRANCH ZERO AND GOTO.
046887,000345:    6316           12521                           TCF      BPL/BMN                               #  13 - BRANCH PLUS AND BRANCH MINUS.
046888,000346:    6317           12474                           TCF      RTB/BHIZ                              #  14 - RETURN TO BASIC AND BRANCH HI ZERO.
046889,000347:    6320           12534                           TCF      CALL/ITA                              #  15 - CALL AND STORE QPRET.
046890,000348:    6321           12543                           TCF      SW/                                   #  16 - SWITCH INSTRUCTIONS AND AVAILABLE.
046891,000349:    6322           12504                           TCF      BOV(B)                                #  17 - BRANCH ON OVERFLOW TO BASIC OR INT.
046892,000350: 

Page 1085

046894,000352:                                                                                                  #           THE FOLLOWING JUMP TABLE APPIES TO UNARY INSTRUCTIONS.
046895,000353: 
046896,000354:    6323                                           COUNT    00/INTER                              
046897,000355: 
046898,000356: 00,2000                                           BANK     0                                     #  00 - EXIT - DETECTED EARLIER.
046899,000357: 00,2000           13207        UNAJUMP            TCF      SQRT                                  #  01 - SQUARE ROOT.
046900,000358: 00,2001           13527                           TCF      SINE                                  #  02 - SIN.
046901,000359: 00,2002           13516                           TCF      COSINE                                #  03 - COS.
046902,000360: 00,2003           13607                           TCF      ARCSIN                                #  04 - ARC SIN.
046903,000361: 00,2004           13611                           TCF      ARCCOS                                #  05 - ARC COS.
046904,000362: 00,2005           13174                           TCF      DSQ                                   #  06 - DP SQUARE.
046905,000363: 00,2006           12116                           TCF      ROUND                                 #  07 - ROUND TO DP.
046906,000364: 
046907,000365: 00,2007           17637                           TCF      COMP                                  #  10 - COMPLEMENT VECTOR OR SCALAR.
046908,000366: 00,2010           13232                           TCF      VDEF                                  #  11 - VECTOR DEFINE.
046909,000367: 00,2011           13023                           TCF      UNIT                                  #  12 - UNIT VECTOR.
046910,000368: 00,2012           13176                           TCF      ABVALABS                              #  13 - LENGTH OF VECTOR OR MAG OF SCALAR.
046911,000369: 00,2013           13245                           TCF      VSQ                                   #  14 - SQUARE OF LENGTH OF VECTOR.
046912,000370: 00,2014           16323                           TCF      STADR                                 #  15 - PUSH UP ON STORE CODE.
046913,000371: 00,2015           13274                           TCF      RVQ                                   #  16 - RETURN VIA QPRET.
046914,000372: 00,2016           13247                           TCF      PUSH                                  #  17 - PUSH MPAC DOWN.
046915,000373: 

Page 1086

046917,000375:                                                                                                  #  SECTION 2  LOAD AND STORE PACKAGE.
046918,000376: 
046919,000377:                                                                                                  #           A SET OF EIGHT STORE CODES IS PROVIDED AS THE PRIMARY METHOD OF STORING THE MULTI-PURPOSE
046920,000378:                                                                                                  #  ACCUMULATOR (MPAC). IF IN THE DANZIG SECTION LOC REFERS TO AN ALGEBRAICALLY POSITIVE WORD, IT IS TAKEN AS A 
046921,000379:                                                                                                  #  STORE CODE WITH A CORRESPONDING ERASABLE ADDRESS. MOST OF THESE CODES ARE TWO ADDRESS, SPECIFYING THAT THE WORD
046922,000380:                                                                                                  #  FOLLOWING THE STORE CODE IS TO BE USED AS AN ADDRESS FROM WHICH TO RE-LOAD MPAC. FOUR OPTIONS ARE AVAILABLE:
046923,000381: 
046924,000382:                                                                                                  #           1. STORE               STORE MPAC. THE E ADDRESS MAY BE INDEXED.
046925,000383:                                                                                                  #           2. STODL               STORE MPAC AND RE-LOAD IT IN DP WITH THE NEXT ADDRESS (THE LOAD MAY BE INDEXED).
046926,000384:                                                                                                  #           3. STOVL               STORE MPAC AND RE-LOAD A VECTOR (AS ABOVE).
046927,000385:                                                                                                  #           4. STCALL              STORE AND DO A CALL (BOTH ADDRESSES MUST BE DIRECT HERE).
046928,000386: 
046929,000387:                                                                                                  #           STODL AND STOVL WILL TAKE FROM THE PUSH-DOWN LIST IF NO LOAD ADDRESS IS GIVEN.
046930,000388: 
046931,000389:    6323                                           BLOCK    3                                     
046932,000390: 
046933,000391:    6323                                           COUNT    03/INTER                              
046934,000392: 
046935,000393:    6323           30165        STADR              CA       BANKSET                               #  THE STADR CODE (PUSHUP UP ON STORE
046936,000394:    6324           54004                           TS       FBANK                                 #  ADDRESS) ENTERS HERE.
046937,000395:    6325           24164                           INCR     LOC                                   
046938,000396:    6326           50164        ITR1               INDEX    LOC                                   #  THE STORECODE WAS STORED COMPLEMENTED TO
046939,000397:    6327           40000                           CS       0                                     #  MAKE IT LOOK LIKE AN OPCODE PAIR.
046940,000398:    6330           67716                           AD       NEGONE                                #  (YUL CANT REMOVE 1 BECAUSE OF EARLY CCS)
046941,000399: 
046942,000400:    6331           54116        DOSTORE            TS       ADDRWD                                
046943,000401:    6332           74372                           MASK     LOW11                                 #  ENTRY FROM DISPATCHER. SAVE THE ERASABLE
046944,000402:    6333           56116                           XCH      ADDRWD                                #  ADDRESS AND JUMP ON THE STORE CODE NO.
046945,000403:    6334           77671                           MASK     B12T14                                
046946,000404:    6335           00006                           EXTEND                                         
046947,000405:    6336           74706                           MP       BIT5                                  #  EACH TRANSFER VECTOR ENTRY IS TWO WORDS.
046948,000406:    6337           50000        ITR0               INDEX    A                                     
046949,000407:    6340           16341                           TCF      STORJUMP                              
046950,000408: 

Page 1087

046952,000410:                                                                                                  #           STORE CODE JUMP TABLE. CALLS THE APPROPRIATE STORING ROUTINE AND EXITS TO DANZIG OR TO ADDRESS WITH
046953,000411:                                                                                                  #  A SUPPLIED OPERATION CODE.
046954,000412: 
046955,000413:                                                                                                  #           STORE STORE,1 AND STORE,2 RETURN TO DANZIG, THUS RESETTING THE EBANK TO ITS STATE AT INTPRET.
046956,000414: 
046957,000415:    6341           06371        STORJUMP           TC       STORE                                 #  STORE.
046958,000416:    6342           16030                           TCF      DANZIG                                #  PICK UP NEW OP CODE(S).
046959,000417:    6343           06363                           TC       STORE,1                               
046960,000418:    6344           16030                           TCF      DANZIG                                
046961,000419:    6345           06366                           TC       STORE,2                               
046962,000420:    6346           16030                           TCF      DANZIG                                
046963,000421: 
046964,000422:    6347           06371                           TC       STORE                                 #  STODL.
046965,000423:    6350           16427                           TCF      DODLOAD                               
046966,000424: 
046967,000425:    6351           06371                           TC       STORE                                 #  STODL WITH INDEXED LOAD ADDRESS.
046968,000426:    6352           16113                           TCF      DODLOAD*                              
046969,000427: 
046970,000428:    6353           06371                           TC       STORE                                 #  STOVL.
046971,000429:    6354           16432                           TCF      DOVLOAD                               
046972,000430: 
046973,000431:    6355           06371                           TC       STORE                                 #  STOVL WITH INDEXED LOAD ADDRESS.
046974,000432:    6356           16435                           TCF      DOVLOAD*                              
046975,000433:    6357           06371                           TC       STORE                                 #  STOTC.
046976,000434:    6360           34723                           CAF      CALLCODE                              
046977,000435:    6361           54020                           TS       CYR                                   
046978,000436:    6362           16221                           TCF      15BITADR                              #  GET A 15 BIT ADDRESS.
046979,000437: 

Page 1088

046981,000439:                                                                                                  #           STORE CODE ADDRESS PROCESSOR.
046982,000440: 
046983,000441:    6363           50120        STORE,1            INDEX    FIXLOC                                
046984,000442:    6364           40046                           CS       X1                                    
046985,000443:    6365           16370                           TCF      PRESTORE                              
046986,000444: 
046987,000445:    6366           50120        STORE,2            INDEX    FIXLOC                                
046988,000446:    6367           40047                           CS       X2                                    
046989,000447:    6370           26116        PRESTORE           ADS      ADDRWD                                #  RESULTANT ADDRESS IS IN ERASABLE.
046990,000448: 
046991,000449:    6371           40116        STORE              CS       ADDRWD                                
046992,000450:    6372           64727                           AD       DEC45                                 
046993,000451:    6373           10000                           CCS      A                                     #  DOES THE ADDRESS POINT TO THE WORK AREA?
046994,000452:    6374           30120                           CA       FIXLOC                                #  YES.
046995,000453:    6375           16402                           TCF      AHEAD5                                
046996,000454:    6376           34744                           CA       OCT1400                               #  NO.  SET EBANK & MAKE UP SUBADDRESS.
046997,000455:    6377           56116                           XCH      ADDRWD                                
046998,000456:    6400           54003                           TS       EBANK                                 
046999,000457:    6401           74373                           MASK     LOW8                                  
047000,000458:    6402           26116        AHEAD5             ADS      ADDRWD                                
047001,000459: 

Page 1089

047003,000461:                                                                                                  #           STORING ROUTINES. STORE DP, TP, OR VECTOR AS INDICATED BY MODE.
047004,000462: 
047005,000463:    6403           00006        STARTSTO           EXTEND                                         #  MPAC,+1 MUST BE STORED IN ANY EVENT.
047006,000464:                                                                                                  #           ITRACE (5) REFERS TO "STARTSTO".
047007,000465:    6404           30155                           DCA      MPAC                                  
047008,000466:    6405           50116                           INDEX    ADDRWD                                
047009,000467:    6406           52001                           DXCH     0                                     
047010,000468: 
047011,000469:    6407           10163                           CCS      MODE                                  
047012,000470:    6410           16423                           TCF      TSTORE                                
047013,000471:    6411           00002                           TC       Q                                     
047014,000472: 
047015,000473:    6412           00006        VSTORE             EXTEND                                         
047016,000474:    6413           30160                           DCA      MPAC       +3                         
047017,000475:    6414           50116                           INDEX    ADDRWD                                
047018,000476:    6415           52003                           DXCH     2                                     
047019,000477: 
047020,000478:    6416           00006                           EXTEND                                         
047021,000479:    6417           30162                           DCA      MPAC       +5                         
047022,000480:    6420           50116                           INDEX    ADDRWD                                
047023,000481:    6421           52005                           DXCH     4                                     
047024,000482:    6422           00002                           TC       Q                                     
047025,000483: 
047026,000484:    6423           30156        TSTORE             CA       MPAC       +2                         
047027,000485:    6424           50116                           INDEX    ADDRWD                                
047028,000486:    6425           54002                           TS       2                                     
047029,000487:    6426           00002                           TC       Q                                     
047030,000488: 

Page 1090

047032,000490:                                                                                                  #           ROUTINES TO BEGIN PROCESSING OF THE SECOND ADDRESS ASSOCIATED WITH ALL STORE-TYPE CODES EXCEPT STORE
047033,000491:                                                                                                  #  ITSELF.
047034,000492: 
047035,000493:    6427           37701        DODLOAD            CAF      DLOADCOD                              
047036,000494:    6430           54020                           TS       CYR                                   
047037,000495:    6431           16055                           TCF      DIRADRES                              #  GO GET A DIRECT ADDRESS.
047038,000496: 
047039,000497:    6432           34674        DOVLOAD            CAF      VLOADCOD                              
047040,000498:    6433           54020                           TS       CYR                                   
047041,000499:    6434           16055                           TCF      DIRADRES                              
047042,000500: 
047043,000501:    6435           36056        DOVLOAD*           CAF      VLOAD*                                
047044,000502:    6436           16114                           TCF      DODLOAD*   +1                         #  PROLOGUE TO INDEX ROUTINE.
047045,000503: 

Page 1091

047047,000505:                                                                                                  #           THE FOLLOWING LOAD INSTRUCTIONS ARE PROVIDED FOR LOADING THE MULTI-PURPOSE ACCUMULATOR MPAC.
047048,000506: 
047049,000507:    6437           50116        TLOAD              INDEX    ADDRWD                                
047050,000508:    6440           30002                           CA       2                                     #  LOAD A TRIPLE PRECISION ARGUMENT INTO
047051,000509:    6441           54156                           TS       MPAC       +2                         #  THE FIRST THREE MPAC REGISTERS, WITH THE
047052,000510:    6442           00006                           EXTEND                                         #  CONTENTS OF THE OTHER FOUR IRRELEVANT.
047053,000511:    6443           50116                           INDEX    ADDRWD                                
047054,000512:    6444           30001                           DCA      0                                     
047055,000513:    6445           52155                           DXCH     MPAC                                  
047056,000514:    6446           34712        TMODE              CAF      ONE                                   
047057,000515:    6447           16027                           TCF      NEWMODE                               #  DECLARE TRIPLE PRECISION MODE.
047058,000516: 
047059,000517:    6450           22007        SLOAD              ZL                                             #  LOAD A SINGLE PRECISION NUMBER INTO
047060,000518:    6451           50116                           INDEX    ADDRWD                                #  MPAC, SETTING MPAC+1,2 TO ZERO. THE
047061,000519:    6452           30000                           CA       0                                     #  CONTENTS OF THE REMAINING MPAC REGISTERS
047062,000520:    6453           16024                           TCF      SLOAD2                                #  ARE IRRELEVANT.
047063,000521: 
047064,000522:    6454           00006        VLOAD              EXTEND                                         #  LOAD A DOUBLE PRECISION VECTOR INTO
047065,000523:    6455           50116                           INDEX    ADDRWD                                #  MPAC,+1, MPAC+3,4, AND MPAC+5,6. THE
047066,000524:    6456           30001                           DCA      0                                     #  CONTENTS OF MPAC +2 ARE IRRELEVANT.
047067,000525:    6457           52155                           DXCH     MPAC                                  
047068,000526: 
047069,000527:    6460           00006        ENDVLOAD           EXTEND                                         #  PDVL COMES HERE TO FINISH UP FOR DP, TP.
047070,000528:    6461           50116                           INDEX    ADDRWD                                
047071,000529:    6462           30003                           DCA      2                                     
047072,000530:    6463           52160                           DXCH     MPAC       +3                         
047073,000531: 
047074,000532:    6464           00006                 +4        EXTEND                                         #  TPDVL FINISHES HERE.
047075,000533:    6465           50116                           INDEX    ADDRWD                                
047076,000534:    6466           30005                           DCA      4                                     
047077,000535:    6467           52162                           DXCH     MPAC       +5                         
047078,000536: 
047079,000537:    6470           44712        VMODE              CS       ONE                                   #  DECLARE VECTOR MODE.
047080,000538:    6471           16027                           TCF      NEWMODE                               
047081,000539: 

Page 1092

047083,000541:                                                                                                  #           THE FOLLOWING INSTRUCTIONS ARE PROVIDED FOR STORING OPERANDS IN THE PUSHDOWN LIST:
047084,000542: 
047085,000543:                                                                                                  #           1.  PUSH               PUSHDOWN AND NO LOAD.
047086,000544:                                                                                                  #           2.  PDDL               PUSHDOWN AND DOUBLE PRECISION LOAD.
047087,000545:                                                                                                  #           3.  PDVL               PUSHDOWN AND VECTOR LOAD.
047088,000546: 
047089,000547:    6472           00006        PDDL               EXTEND                                         
047090,000548:    6473           50116                           INDEX    ADDRWD                                #  LOAD MPAC,+1, PUSHING THE FORMER
047091,000549:    6474           30001                           DCA      0                                     #  CONTENTS DOWN.
047092,000550:    6475           52155                           DXCH     MPAC                                  
047093,000551:    6476           50166                           INDEX    PUSHLOC                               
047094,000552:    6477           52001                           DXCH     0                                     
047095,000553: 
047096,000554:    6500           50163                           INDEX    MODE                                  #  ADVANCE THE PUSHDOWN POINTER APPRO-
047097,000555:    6501           36213                           CAF      NO.WDS                                #  PRIATELY.
047098,000556:    6502           26166                           ADS      PUSHLOC                               
047099,000557: 
047100,000558:    6503           10163                           CCS      MODE                                  
047101,000559:    6504           16521                           TCF      ENDTPUSH                              
047102,000560:    6505           16517                           TCF      ENDDPUSH                              
047103,000561: 
047104,000562:    6506           54163                           TS       MODE                                  #  NOW DP.
047105,000563:    6507           54156        ENDVPUSH           TS       MPAC       +2                         
047106,000564:    6510           52160                           DXCH     MPAC       +3                         #  PUSH DOWN THE REST OF THE VECTOR HERE.
047107,000565:    6511           50166                           INDEX    PUSHLOC                               
047108,000566:    6512           51775                           DXCH     0          -4                         
047109,000567: 
047110,000568:    6513           52162                           DXCH     MPAC       +5                         
047111,000569:    6514           50166                           INDEX    PUSHLOC                               
047112,000570:    6515           51777                           DXCH     0          -2                         
047113,000571: 
047114,000572:    6516           16030                           TCF      DANZIG                                
047115,000573: 
047116,000574:    6517           54156        ENDDPUSH           TS       MPAC       +2                         #  SET MPAC +2 TO ZERO AND EXIT ON DP.
047117,000575:    6520           16030                           TCF      DANZIG                                
047118,000576: 
047119,000577:    6521           54163        ENDTPUSH           TS       MODE                                  
047120,000578:    6522           56156                           XCH      MPAC       +2                         #  ON TRIPLE, SET MPAC +2 TO ZERO, PUSHING
047121,000579:    6523           50166                 +2        INDEX    PUSHLOC                               #  DOWN THE OLD CONTENTS
047122,000580:    6524           53777                           TS       0          -1                         
047123,000581:    6525           16030                           TCF      DANZIG                                
047124,000582: 

Page 1093

047126,000584:                                                                                                  #           PDVL - PUSHDOWN AND VECTOR LOAD.
047127,000585: 
047128,000586:    6526           00006        PDVL               EXTEND                                         #  RELOAD MPAC AND PUSH DOWN ITS CONTENTS.
047129,000587:    6527           50116                           INDEX    ADDRWD                                
047130,000588:    6530           30001                           DCA      0                                     
047131,000589:    6531           52155                           DXCH     MPAC                                  
047132,000590:    6532           50166                           INDEX    PUSHLOC                               
047133,000591:    6533           52001                           DXCH     0                                     
047134,000592: 
047135,000593:    6534           50163                           INDEX    MODE                                  #  ADVANCE THE PUSHDOWN POINTER.
047136,000594:    6535           36213                           CAF      NO.WDS                                
047137,000595:    6536           26166                           ADS      PUSHLOC                               
047138,000596: 
047139,000597:    6537           10163                           CCS      MODE                                  #  TEST PAST MODE.
047140,000598:    6540           16557                           TCF      TPDVL                                 
047141,000599:    6541           16460                           TCF      ENDVLOAD                              #  JUST LOAD LAST FOUR REGISTERS ON DP.
047142,000600: 
047143,000601:    6542           00006        VPDVL              EXTEND                                         #  PUSHDOWN AND RE-LOAD LAST TWO COMPONENTS
047144,000602:    6543           50116                           INDEX    ADDRWD                                
047145,000603:    6544           30003                           DCA      2                                     
047146,000604:    6545           52160                           DXCH     MPAC       +3                         
047147,000605:    6546           50166                           INDEX    PUSHLOC                               
047148,000606:    6547           51775                           DXCH     0          -4                         
047149,000607: 
047150,000608:    6550           00006                           EXTEND                                         
047151,000609:    6551           50116                           INDEX    ADDRWD                                
047152,000610:    6552           30005                           DCA      4                                     
047153,000611:    6553           52162                           DXCH     MPAC       +5                         
047154,000612:    6554           50166                           INDEX    PUSHLOC                               
047155,000613:    6555           51777                           DXCH     0          -2                         
047156,000614: 
047157,000615:    6556           16030                           TCF      DANZIG                                
047158,000616: 
047159,000617:    6557           00006        TPDVL              EXTEND                                         #  ON TP, WE MUST LOAD THE Y COMPONENT
047160,000618:    6560           50116                           INDEX    ADDRWD                                #  BEFORE STORING MPAC +2 INCASE THIS IS A
047161,000619:    6561           30003                           DCA      2                                     #  PUSHUP.
047162,000620:    6562           52160                           DXCH     MPAC       +3                         
047163,000621: 
047164,000622:    6563           30156                           CA       MPAC       +2                         
047165,000623:    6564           50166                           INDEX    PUSHLOC                               #  IN DP.
047166,000624:    6565           53777                           TS       0          -1                         
047167,000625:    6566           16464                           TCF      ENDVLOAD   +4                         
047168,000626: 
047169,000627:                                                                                                  #           SSP (STORE SINGLE PRECISION) IS EXECUTED HERE.
047170,000628: 
047171,000629:    6567           24164        SSP                INCR     LOC                                   #  PICK UP THE WORD FOLLOWING THE GIVEN
047172,000630:    6570           50164                           INDEX    LOC                                   #  ADDRESS AND STORE IT AT X.
047173,000631:    6571           30000                           CA       0                                     
047174,000632:    6572           50116        STORE1             INDEX    ADDRWD                                #  SOME INDEX AND MISCELLANEOUS OPS END
047175,000633:    6573           54000                           TS       0                                     #  HERE.

Page 1094

047177,000635:    6574           16030                           TCF      DANZIG                                
047178,000636: 

Page 1095

047180,000638:                                                                                                  #  SEQUENCE CHANGING AND SUBROUTINE CALLING OPTIONS.
047181,000639: 
047182,000640:                                                                                                  #           THE FOLLOWING OPERATIONS ARE AVAILABLE FOR SEQUENCING CHANGING, BRANCHING, AND CALLING SUBROUTINES:
047183,000641: 
047184,000642:                                                                                                  #           1.  GOTO               GO TO.
047185,000643:                                                                                                  #           2.  CALL               CALL SUBROUTINE SETTING QPRET.
047186,000644:                                                                                                  #           3.  CGOTO              COMPUTED GO TO.
047187,000645:                                                                                                  #           4.  CCALL              COMPUTED CALL.
047188,000646:                                                                                                  #           7.  BPL                BRANCH IF MPAC POSITIVE OR ZERO.
047189,000647:                                                                                                  #           8.  BZE                BRANCH IF MPAC ZERO.
047190,000648:                                                                                                  #           9.  BMN                BRANCH IF MPAC NEGATIVE NON-ZERO.
047191,000649: 
047192,000650:    6575           24164        CCALL              INCR     LOC                                   #  MAINTAIN LOC FOR QPRET COMPUTATION.
047193,000651:    6576           50164                           INDEX    LOC                                   
047194,000652:    6577           30000                           CAF      0                                     #  GET BASE ADDRESS OF CADR LIST.
047195,000653:    6600           50116                           INDEX    ADDRWD                                
047196,000654:    6601           60000                           AD       0                                     #  ADD INCREMENT.
047197,000655:    6602           54004                           TS       FBANK                                 #  SELECT DESIRED CADR.
047198,000656:    6603           74747                           MASK     LOW10                                 
047199,000657:    6604           50000                           INDEX    A                                     
047200,000658:    6605           32000                           CAF      10000                                 
047201,000659:    6606           54117                           TS       POLISH                                
047202,000660: 
047203,000661:    6607           30165        CALL               CA       BANKSET                               #  FOR ANY OF THE CALL OPTIONS, MAKE UP THE
047204,000662:    6610           74364                           MASK     BANKMASK                              #  ADDRESS OF THE NEXT OP-CODE PAIR/STORE
047205,000663:    6611           64364                           AD       BANKMASK                              #  CODE AND LEAVE IT IN QPRET.  NOTE THAT
047206,000664:    6612           60164                           AD       LOC                                   #  BANKMASK = -(2000 - 1).
047207,000665:    6613           50120                           INDEX    FIXLOC                                
047208,000666:    6614           54052                           TS       QPRET                                 
047209,000667: 
047210,000668:    6615           30117        GOTO               CA       POLISH                                #  BASIC BRANCHING SEQUENCE.
047211,000669:    6616           77711                 +1        MASK     HIGH4                                 
047212,000670:    6617           00006                           EXTEND                                         
047213,000671:    6620           16631                           BZF      GOTOERS                               #  SEE IF ADDRESS POINTS TO FIXED OR ERAS.
047214,000672:    6621           30165                 +4        CA       BANKSET                               #  SET EBANK PART OF BBANK. NEXT, SET UP
047215,000673:    6622           54006                           TS       BBANK                                 #  FBANK. THE COMBINATION IS PICKED UP &
047216,000674:    6623           30117                           CA       POLISH                                #  PUT INTO BANKSET AT INTPRET +2.
047217,000675:    6624           54004                           TS       FBANK                                 
047218,000676:    6625           74747                           MASK     LOW10                                 
047219,000677:    6626           64700                           AD       2K                                    
047220,000678:    6627           54164                           TS       LOC                                   
047221,000679:    6630           16011                           TCF      INTPRET    +3                         
047222,000680: 
047223,000681:    6631  E3,1400                                  EBANK=   1400                                  #  SO YUL DOESN'T CUSS THE "CA 1400" BELOW.
047224,000682: 
047225,000683:    6631           30117        GOTOERS            CA       POLISH                                #  THE GIVEN ADDRESS IS IN ERASABLE - SEE
047226,000684:    6632           66220                           AD       -ENDVAC                               #  IF RELATIVE TO THE WORK AREA.
047227,000685:    6633           10000                           CCS      A                                     
047228,000686:    6634           30117                           CA       POLISH                                #  GENERAL ERASABLE.
047229,000687:    6635           16644                           TCF      GOTOGE                                

Page 1096

047231,000689:    6636           30120                           CA       FIXLOC                                #  WORK AREA.
047232,000690:    6637           60117                           AD       POLISH                                
047233,000691:    6640           50000                           INDEX    A                                     #  USE THE GIVEN ADDRESS AS THE ADDRESS OF
047234,000692:    6641           30000                           CA       0                                     #  THE BRANCH ADDRESS.
047235,000693:    6642           54117                           TS       POLISH                                
047236,000694:    6643           16616                           TCF      GOTO       +1                         #  ALLOWS ARBITRARY INDIRECTNESS LEVELS.
047237,000695: 
047238,000696:    6644           54003        GOTOGE             TS       EBANK                                 
047239,000697:    6645           74373                           MASK     LOW8                                  
047240,000698:    6646           50000                           INDEX    A                                     #  USE THE GIVEN ADDRESS AS THE ADDRESS OF
047241,000699:    6647           31400                           CA       1400                                  #  THE BRANCH ADDRESS.
047242,000700:    6650           54117                           TS       POLISH                                
047243,000701:    6651           16616                           TCF      GOTO       +1                         
047244,000702: 
047245,000703:    6652           50164        CGOTO              INDEX    LOC                                   #  COMPUTED GO TO. PICK UP ADDRESS OF CADR
047246,000704:    6653           30001                           CA       1                                     #  LIST.
047247,000705:    6654           50116                           INDEX    ADDRWD                                #  ADD MODIFIER.
047248,000706:    6655           60000                           AD       0                                     
047249,000707:    6656           54004                           TS       FBANK                                 #  SELECT GOTO ADDRESS.
047250,000708:    6657           74747                           MASK     LOW10                                 
047251,000709:    6660           50000                           INDEX    A                                     
047252,000710:    6661           32000                           CA       10000                                 
047253,000711:    6662           54117                           TS       POLISH                                
047254,000712:    6663           16616                           TCF      GOTO       +1                         #  WITH ADDRESS IN A.
047255,000713: 
047256,000714:    6664           30165        SWBRANCH           CA       BANKSET                               #  SWITCH INSTRUCTIONS WHICH ELECT TO
047257,000715:    6665           54004                           TS       FBANK                                 #  BRANCH COME HERE TO DO SO.
047258,000716:    6666           50164                           INDEX    LOC                                   
047259,000717:    6667           30001                           CA       1                                     
047260,000718:    6670           54117                           TS       POLISH                                
047261,000719:    6671           16616                           TCF      GOTO       +1                         
047262,000720: 

Page 1097

047264,000722:                                                                                                  #           TRIPLE PRECISION BRANCHING ROUTINE. IF CALLING TC IS AT L, RETURN IS AS FOLLOWS:
047265,000723: 
047266,000724:                                                                                                  #           L+1  IF MPAC IS GREATER THAN ZERO.
047267,000725:                                                                                                  #           L+2  IF MPAC IS EQUAL TO +0 OR -0.
047268,000726:                                                                                                  #           L+3  IF MPAC IS LESS THAN ZERO.
047269,000727: 
047270,000728:    6672           10154        BRANCH             CCS      MPAC                                  
047271,000729:    6673           00002                           TC       Q                                     
047272,000730:    6674           16676                           TCF      +2                                    #  ON ZERO.
047273,000731:    6675           16710                           TCF      NEG                                   
047274,000732: 
047275,000733:    6676           10155                           CCS      MPAC       +1                         
047276,000734:    6677           00002                           TC       Q                                     
047277,000735:    6700           16702                           TCF      +2                                    
047278,000736:    6701           16710                           TCF      NEG                                   
047279,000737: 
047280,000738:    6702           10156                           CCS      MPAC       +2                         
047281,000739:    6703           00002                           TC       Q                                     
047282,000740:    6704           16706                           TCF      +2                                    
047283,000741:    6705           16710                           TCF      NEG                                   
047284,000742: 
047285,000743:    6706           50002        Q+1                INDEX    Q                                     
047286,000744:    6707           00001                           TC       1                                     
047287,000745: 
047288,000746:    6710           50002        NEG                INDEX    Q                                     #  IF FIRST NON-ZERO REGISTER WAS NEGATIVE.
047289,000747:    6711           00002                           TC       2                                     
047290,000748: 
047291,000749: 
047292,000750:    6712     6710               Q+2                =        NEG                                   
047293,000751: 
047294,000752:                                                                                                  #           ITRACE (3) REFERS TO "EXIT".
047295,000753:    6712           30165        EXIT               CA       BANKSET                               #  RESTORE USER'S BANK SETTING, AND LEAVE
047296,000754:    6713           54006                           TS       BBANK                                 #  INTERPRETIVE MODE.
047297,000755:    6714           50164                           INDEX    LOC                                   
047298,000756:    6715           00001                           TC       1                                     
047299,000757: 

Page 1098

047301,000759:                                                                                                  #  SECTION 3 - ADD/SUBTRACT PACKAGE.
047302,000760: 
047303,000761:                                                                                                  #           THE FOLLOWING OPERATIONS ARE PROVIDED FOR ADDING TO AND SUBTRACTING FROM THE MULTI-PURPOSE ACCUMULATOR
047304,000762:                                                                                                  #  MPAC:
047305,000763: 
047306,000764:                                                                                                  #           1.  DAD                DOUBLE PRECISION ADD.
047307,000765:                                                                                                  #           2.  DSU                DOUBLE PRECISION SUBTRACT.
047308,000766:                                                                                                  #           3.  BDSU               DOUBLE PRECISION SUBTRACT FROM.
047309,000767: 
047310,000768:                                                                                                  #           4.  TAD                TRIPLE PRECISION ADD.
047311,000769: 
047312,000770:                                                                                                  #           5.  VAD                VECTOR ADD.
047313,000771:                                                                                                  #           6.  VSU                VECTOR SUBTRACT.
047314,000772:                                                                                                  #           7.  BVSU               VECTOR SUBTRACT FROM.
047315,000773: 
047316,000774:                                                                                                  #  THE INTERPRETIVE OVERFLOW INDICATOR OVFIND IS SET NON-ZERO IF OVERFLOW OCCURS IN ANY OF THE ABOVE.
047317,000775: 
047318,000776:    6716           34674        VSU                CAF      BIT15                                 #  CHANGES 0 TO DCS.
047319,000777:    6717           16721                           TCF      +2                                    
047320,000778: 
047321,000779:    6720           34371        VAD                CAF      PRIO30                                #  CHANGES 0 TO DCA.
047322,000780:    6721           26116                           ADS      ADDRWD                                
047323,000781:    6722           00006                           EXTEND                                         
047324,000782:    6723           50116                           INDEX    ADDRWD                                
047325,000783:    6724           00003                           READ     HISCALAR                              #  DCA  2   OR   DCS  2
047326,000784:    6725           20160                           DAS      MPAC       +3                         
047327,000785:    6726           00006                           EXTEND                                         #  CHECK OVERFLOW.
047328,000786:    6727           16731                           BZF      +2                                    
047329,000787:    6730           06763                           TC       OVERFLWY                              
047330,000788: 
047331,000789:    6731           00006                           EXTEND                                         
047332,000790:    6732           50116                           INDEX    ADDRWD                                
047333,000791:    6733           00005                           READ     CHAN5                                 #  DCA  4   OR   DCS  4
047334,000792:    6734           20162                           DAS      MPAC       +5                         
047335,000793:    6735           00006                           EXTEND                                         
047336,000794:    6736           16740                           BZF      +2                                    
047337,000795:    6737           06760                           TC       OVERFLWZ                              
047338,000796: 
047339,000797:    6740           00006                           EXTEND                                         
047340,000798:    6741           50116                           INDEX    ADDRWD                                
047341,000799:    6742           00001                           READ     LCHAN                                 #  DCA  0   OR   DCS  0
047342,000800:    6743           16747                           TCF      ENDVXV                                
047343,000801: 
047344,000802:    6744           00006        DAD                EXTEND                                         
047345,000803:    6745           50116                           INDEX    ADDRWD                                
047346,000804:    6746           30001                           DCA      0                                     
047347,000805:    6747           20155        ENDVXV             DAS      MPAC                                  #  VXV FINISHES HERE.
047348,000806:    6750           00006                           EXTEND                                         
047349,000807:    6751           16030                           BZF      DANZIG                                

Page 1099

047351,000809:    6752           06766        SETOVF             TC       OVERFLOW                              
047352,000810:    6753           16030                           TCF      DANZIG                                
047353,000811: 

Page 1100

047355,000813:    6754           00006        DSU                EXTEND                                         
047356,000814:    6755           50116                           INDEX    ADDRWD                                
047357,000815:    6756           40001                           DCS      0                                     
047358,000816:    6757           16747                           TCF      ENDVXV                                
047359,000817: 
047360,000818:    6760           54001        OVERFLWZ           TS       L                                     #  ENTRY FOR THIRD COMPONENT.
047361,000819:    6761           34715                           CAF      FIVE                                  
047362,000820:    6762           16765                           TCF      +3                                    
047363,000821: 
047364,000822:    6763           54001        OVERFLWY           TS       L                                     #  ENTRY FOR SECOND COMPONENT.
047365,000823:    6764           36214                           CAF      THREE                                 
047366,000824:    6765           56001                           XCH      L                                     
047367,000825: 
047368,000826:    6766           50000        OVERFLOW           INDEX    A                                     #  ENTRY FOR 1ST COMP OR DP (L=0).
047369,000827:    6767           44673                           CS       LIMITS                                #  PICK UP POSMAX OR NEGMAX.
047370,000828:    6770           54130                           TS       BUF                                   
047371,000829:    6771           00006                           EXTEND                                         
047372,000830:    6772           24000                           AUG      A                                     #  FORCE OVERFLOW.
047373,000831:    6773           50001                           INDEX    L                                     
047374,000832:    6774           26155                           ADS      MPAC       +1                         
047375,000833:    6775           54007                           TS       7                                     
047376,000834:    6776           34714                           CAF      ZERO                                  
047377,000835:    6777           60130                           AD       BUF                                   
047378,000836:    7000           50001                           INDEX    L                                     
047379,000837:    7001           26154                           ADS      MPAC                                  
047380,000838:    7002           54007                           TS       7                                     
047381,000839:    7003           00002                           TC       Q                                     #  NO OVERFLOW EXIT.
047382,000840:    7004           17121                           TCF      SETOVF2                               #  SET OVFIND AND EXIT.
047383,000841: 
047384,000842:    7005           00006        BVSU               EXTEND                                         
047385,000843:    7006           50116                           INDEX    ADDRWD                                
047386,000844:    7007           30003                           DCA      2                                     
047387,000845:    7010           52160                           DXCH     MPAC       +3                         
047388,000846:    7011           00006                           EXTEND                                         
047389,000847:    7012           40001                           DCOM                                           
047390,000848:    7013           20160                           DAS      MPAC       +3                         
047391,000849:    7014           00006                           EXTEND                                         
047392,000850:    7015           17017                           BZF      +2                                    
047393,000851:    7016           06763                           TC       OVERFLWY                              
047394,000852: 
047395,000853:    7017           00006                           EXTEND                                         
047396,000854:    7020           50116                           INDEX    ADDRWD                                
047397,000855:    7021           30005                           DCA      4                                     
047398,000856:    7022           52162                           DXCH     MPAC       +5                         
047399,000857:    7023           00006                           EXTEND                                         
047400,000858:    7024           40001                           DCOM                                           
047401,000859:    7025           20162                           DAS      MPAC       +5                         
047402,000860:    7026           00006                           EXTEND                                         
047403,000861:    7027           17031                           BZF      +2                                    
047404,000862:    7030           06760                           TC       OVERFLWZ                              

Page 1101

047406,000864:    7031           00006        BDSU               EXTEND                                         
047407,000865:    7032           50116                           INDEX    ADDRWD                                
047408,000866:    7033           30001                           DCA      0                                     
047409,000867:    7034           52155                           DXCH     MPAC                                  
047410,000868:    7035           00006                           EXTEND                                         
047411,000869:    7036           40001                           DCOM                                           
047412,000870:    7037           16747                           TCF      ENDVXV                                
047413,000871: 

Page 1102

047415,000873:                                                                                                  #           TRIPLE PRECISION ADD ROUTINE.
047416,000874: 
047417,000875:    7040           00006        TAD                EXTEND                                         
047418,000876:    7041           50116                           INDEX    ADDRWD                                
047419,000877:    7042           30002                           DCA      1                                     #  ADD MINOR PARTS FIRST.
047420,000878:    7043           20156                           DAS      MPAC       +1                         
047421,000879:    7044           50116                           INDEX    ADDRWD                                
047422,000880:    7045           60000                           AD       0                                     
047423,000881:    7046           60154                           AD       MPAC                                  
047424,000882:    7047           54154                           TS       MPAC                                  
047425,000883:    7050           16030                           TCF      DANZIG                                
047426,000884: 
047427,000885:    7051           16752                           TCF      SETOVF                                #  SET OVFIND IF SUCH OCCURS.
047428,000886: 

Page 1103

047430,000888:                                                                                                  #  ARITHMETIC SUBROUTINES REQUIRED IN FIXED-FIXED.
047431,000889: 
047432,000890:                                                                                                  #           1.  DMPSUB     DOUBLE PRECISION MULTIPLY. MULTIPLY THE CONTENTS OF MPAC,+1 BY THE DP WORD WHOSE ADDRESS
047433,000891:                                                                                                  #                          IS IN ADDRWD AND LEAVE A TRIPLE PRECISION RESULT IN MPAC.
047434,000892:                                                                                                  #           2.  ROUNDSUB   ROUND THE TRIPLE PRECISON CONTENTS OF MPAC TO DOUBLE PRECISION.
047435,000893:                                                                                                  #           3.  DOTSUB     TAKE THE DOT PRODUCT OF THE VECTOR IN MPAC AND THE VECTOR WHOSE ADDRESS IS IN ADDRWD
047436,000894:                                                                                                  #                          AND LEAVE THE TRIPLE PRECISION RESULT IN MPAC.
047437,000895:                                                                                                  #           4.  POLY       USING THE CONTENTS OF MPAC AS A DP ARGUMENT, EVALUATE THE POLYNOMIAL WHOSE DEGREE AND
047438,000896:                                                                                                  #                          COEFFICIENTS IMMEDIATELY FOLLOW THE TC POLY INSTRUCTION (SEE ROUTINE FOR DETAILS.)
047439,000897: 
047440,000898: 
047441,000899:    7052           50002        DMP                INDEX    Q                                     #  BASIC SUBROUTINE FOR USE BY PINBALL, ETC
047442,000900:    7053           30000                           CAF      0                                     #  ADRES OF ARGUMENT FOLLOWS  TC DMP .
047443,000901:    7054           24002                           INCR     Q                                     
047444,000902:    7055           54116                 -1        TS       ADDRWD                                #  (PROLOGUE FOR SETTING ADDRWD.)
047445,000903: 
047446,000904:    7056           50116        DMPSUB             INDEX    ADDRWD                                #  GET MINOR PART OF OPERAND AT C(ADDRWD).
047447,000905:    7057           30001                           CA       1                                     
047448,000906:    7060           54156                           TS       MPAC       +2                         #  THIS WORKS FOR SQUARING MPAC AS WELL.
047449,000907:    7061           34714                           CAF      ZERO                                  #  SET MPAC +1 TO ZERO SO WE CAN ACCUMULATE
047450,000908:    7062           56155                           XCH      MPAC       +1                         #  THE PARTIAL PRODUCTS WITH DAS
047451,000909:    7063           54135                           TS       MPTEMP                                #  INSTRUCTIONS.
047452,000910:    7064           00006                           EXTEND                                         
047453,000911:    7065           70156                           MP       MPAC       +2                         #  MINOR OF MPAC X MINOR OF C(ADDRWD).
047454,000912: 
047455,000913:    7066           56156                           XCH      MPAC       +2                         #  DISCARD MINOR PART OF ABOVE RESULT AND
047456,000914:    7067           00006                           EXTEND                                         #  FORM MAJOR OF MPAC X MINOR OF C(ADDRWD).
047457,000915:    7070           70154                           MP       MPAC                                  
047458,000916:    7071           20156                           DAS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
047459,000917: 
047460,000918:    7072           50116                           INDEX    ADDRWD                                #  GET MAJOR PART OF ARGUMENT AT C(ADDRWD).
047461,000919:    7073           30000                           CA       0                                     
047462,000920:    7074           56135                           XCH      MPTEMP                                #  SAVE AND BRING OUT MINOR OF MPAC.
047463,000921:    7075           00006        DMPSUB2            EXTEND                                         
047464,000922:    7076           70135                           MP       MPTEMP                                #  MAJOR OF C(ADDRWD) X MINOR OF MPAC.
047465,000923:    7077           20156                           DAS      MPAC       +1                         #  ACCUMULATE, SETTING A TO NET OVERFLOW.
047466,000924: 
047467,000925:    7100           56154                           XCH      MPAC                                  #  SETTING MPAC TO 0 OR +-1.
047468,000926:    7101           00006                           EXTEND                                         
047469,000927:    7102           70135                           MP       MPTEMP                                #  MAJOR OF MPAC X MAJOR OF C(ADDRWD).
047470,000928:    7103           20155                           DAS      MPAC                                  #  GUARANTEED NO OVERFLOW.
047471,000929:    7104           00002                           TC       Q                                     #  49 MCT = .573 MS. INCLUDING RETURN.
047472,000930: 

Page 1104

047474,000932:                                                                                                  #           ROUND MPAC TO DOUBLE PRECISION, SETTING OVFIND ON THE RARE EVENT OF OVERFLOW.
047475,000933: 
047476,000934:    7105           34714        ROUNDSUB           CAF      ZERO                                  #  SET MPAC +2 = 0 FOR SCALARS AND CHANGE
047477,000935:    7106           54163                 +1        TS       MODE                                  #  MODE TO DP.
047478,000936: 
047479,000937:    7107           56156        VROUND             XCH      MPAC       +2                         #  BUT WE NEEDNT TAKE THE TIME FOR VECTORS.
047480,000938:    7110           60000                           DOUBLE                                         
047481,000939:    7111           54001                           TS       L                                     
047482,000940:    7112           00002                           TC       Q                                     
047483,000941: 
047484,000942:    7113           60155                           AD       MPAC       +1                         #  ADD ROUNDING BIT IF MPAC +2 WAS GREATER
047485,000943:    7114           54155                           TS       MPAC       +1                         #  THAN .5 IN MAGNITUDE.
047486,000944:    7115           00002                           TC       Q                                     
047487,000945: 
047488,000946:    7116           60154                           AD       MPAC                                  #  PROPAGATE INTERFLOW.
047489,000947:    7117           54154                           TS       MPAC                                  
047490,000948:    7120           00002                           TC       Q                                     
047491,000949: 
047492,000950:    7121           54121        SETOVF2            TS       OVFIND                                #  (RARE).
047493,000951:    7122           00002                           TC       Q                                     
047494,000952: 

Page 1105

047496,000954:                                                                                                  #           THE DOT PRODUCT SUBROUTINE USUALLY FORMS THE DOT PRODUCT OF THE VECTOR IN MPAC WITH A STANDARD SIX
047497,000955:                                                                                                  #  REGISTER VECTOR WHOSE ADDRESS IS IN ADDRWD. IN THIS CASE C(DOTINC) ARE SET TO 2. VXM, HOWEVER, SETS C(DOTINC) TO
047498,000956:                                                                                                  #  6 SO THAT DOTSUB DOTS MPAC WITH A COLUMN VECTOR OF THE MATRIX IN QUESTION IN THIS CASE.
047499,000957: 
047500,000958:    7123           34711        PREDOT             CAF      TWO                                   #  PROLOGUE TO SET DOTINC TO 2.
047501,000959:    7124           54136                           TS       DOTINC                                
047502,000960: 
047503,000961:    7125           00006        DOTSUB             EXTEND                                         
047504,000962:    7126           22137                           QXCH     DOTRET                                #  SAVE RETURN.
047505,000963:    7127           07056                           TC       DMPSUB                                #  DOT X COMPONENTS.
047506,000964:    7130           52160                           DXCH     MPAC       +3                         #  POSITION Y COMPONENT OF MPAC FOR
047507,000965:    7131           52155                           DXCH     MPAC                                  #  MULTIPLICATION WHILE SAVING RESULT IN
047508,000966:    7132           52131                           DXCH     BUF                                   #  THREE WORD BUFFER, BUF.
047509,000967:    7133           30156                           CA       MPAC       +2                         
047510,000968:    7134           54132                           TS       BUF        +2                         
047511,000969: 
047512,000970:    7135           30136                           CA       DOTINC                                #  ADVANCE ADDRWD TO Y COMPONENT OF
047513,000971:    7136           26116                           ADS      ADDRWD                                #  OTHER ARGUMENT.
047514,000972:    7137           07056                           TC       DMPSUB                                
047515,000973:    7140           52156                           DXCH     MPAC       +1                         #  ACCUMULATE PARTIAL PRODUCTS.
047516,000974:    7141           20132                           DAS      BUF        +1                         
047517,000975:    7142           60154                           AD       MPAC                                  
047518,000976:    7143           60130                           AD       BUF                                   
047519,000977:    7144           54130                           TS       BUF                                   
047520,000978:    7145           17147                           TCF      +2                                    
047521,000979:    7146           54121                           TS       OVFIND                                #  IF OVERFLOW OCCURS.
047522,000980: 
047523,000981:    7147           52162                           DXCH     MPAC       +5                         #  MULTIPLY Z COMPONENTS.
047524,000982:    7150           52155                           DXCH     MPAC                                  
047525,000983:    7151           30136                           CA       DOTINC                                
047526,000984:    7152           26116                           ADS      ADDRWD                                
047527,000985:    7153           07056                           TC       DMPSUB                                
047528,000986:    7154           52132        ENDDOT             DXCH     BUF        +1                         #  LEAVE FINAL ACCUMULATION IN MPAC.
047529,000987:    7155           20156                           DAS      MPAC       +1                         
047530,000988:    7156           60154                           AD       MPAC                                  
047531,000989:    7157           60130                           AD       BUF                                   
047532,000990:    7160           54154                           TS       MPAC                                  
047533,000991:    7161           00137                           TC       DOTRET                                
047534,000992: 
047535,000993:    7162           06766                           TC       OVERFLOW                              #  ON OVERFLOW HERE.
047536,000994:    7163           00137                           TC       DOTRET                                
047537,000995: 

Page 1106

047539,000997:                                                                                                  #  DOUBLE PRECISION POLYNOMIAL EVALUATOR
047540,000998: 
047541,000999:                                                                                                  #                                     N        N-1
047542,001000:                                                                                                  #           THIS ROUTINE EVALUATES A X  + A   X    + ... + A  X + A  LEAVING THE DP RESULT IN MPAC ON EXIT.
047543,001001:                                                                                                  #                                   N      N-1              1      0
047544,001002: 
047545,001003:                                                                                                  #  THE ROUTINE HAS TWO ENTRIES
047546,001004: 
047547,001005:                                                                                                  #           1. ENTRY THRU POWRSERS. THE COEFFICIENTS MAY BE EITHER IN FIXED OR ERASABLE, THE CALL IS BY
047548,001006:                                                                                                  #              TC POWRSERS, AND THE RETURN IS TO LOC(TC POWRSERS)+1. THE ENTERING DATA MUST BE AS FOLLOWS
047549,001007: 
047550,001008:                                                                                                  #                                          A        SP     LOC-3           ADDRESS FOR REFERENCING COEF TABLE
047551,001009:                                                                                                  #                                          L        SP     N-1             N IS THE DEGREE OF THE POWER SERIES
047552,001010:                                                                                                  #                                          MPAC     DP     X               ARGUMENT
047553,001011: 
047554,001012:                                                                                                  #                                          LOC-2N   DP     A(0)
047555,001013:                                                                                                  #                                                   ...
047556,001014:                                                                                                  #                                          LOC      DP     A(N)
047557,001015: 
047558,001016:                                                                                                  #           2. ENTRY THRU POLY. THE CALL TO POLY AND THE ENTERING DATA MUST BE AS FOLLOWS
047559,001017: 
047560,001018:                                                                                                  #                                          MPAC     DP     X               ARGUMENT
047561,001019: 
047562,001020:                                                                                                  #                                          LOC      TC     POLY
047563,001021:                                                                                                  #                                          LOC+1    SP     N-1
047564,001022:                                                                                                  #                                          LOC+2    DP     A(0)
047565,001023:                                                                                                  #                                                   ...
047566,001024:                                                                                                  #                                          LOC+2N+2 DP     A(N)            RETURN IS TO LOC+2N+4
047567,001025: 
047568,001026:    7164           00006        POWRSERS           EXTEND                                         
047569,001027:    7165           22141                           QXCH     POLYRET                               #  RETURN ADDRESS
047570,001028:    7166           54117                           TS       POLISH                                #  POWER SERIES ADDRESS
047571,001029:    7167           22140                           LXCH     POLYCNT                               #  N-1 TO COUNTER
047572,001030:    7170           17201                           TCF      POLYCOM                               #  SKIP SET UP BY POLY
047573,001031: 
047574,001032:    7171           50002        POLY               INDEX    Q                                     
047575,001033:    7172           30000                           CAF      0                                     
047576,001034:    7173           54140                           TS       POLYCNT                               #  N-1 TO COUNTER
047577,001035:    7174           60000                           DOUBLE                                         
047578,001036:    7175           60002                           AD       Q                                     
047579,001037:    7176           54117                           TS       POLISH                                #  L(A(N))-3 TO POLISH
047580,001038:    7177           64715                           AD       FIVE                                  
047581,001039:    7200           54141                           TS       POLYRET                               #  STORE RETURN ADDRESS
047582,001040: 
047583,001041:    7201           36242        POLYCOM            CAF      LVBUF                                 #  INCOMING X WILL BE MOVED TO VBUF, SO
047584,001042:    7202           54116                           TS       ADDRWD                                #  SET ADDRWD SO DMPSUB WILL MPY BY VBUF.
047585,001043: 
047586,001044:    7203           00006                           EXTEND                                         
047587,001045:    7204           50117                           INDEX    POLISH                                
047588,001046:    7205           30004                           DCA      3                                     
047589,001047: 

Page 1107

047591,001049:    7206           52155                           DXCH     MPAC                                  #  LOAD A(N) INTO MPAC,
047592,001050:    7207           52123                           DXCH     VBUF                                  #  SAVING X IN VBUF
047593,001051:    7210           17214                           TCF      POLY2                                 
047594,001052: 
047595,001053:    7211           54140        POLYLOOP           TS       POLYCNT                               #  SAVE DECREMENTED LOOP COUNTER
047596,001054:    7212           44711                           CS       TWO                                   
047597,001055:    7213           26117                           ADS      POLISH                                #  REGRESS COEFFICIENT POINTER
047598,001056: 
047599,001057:    7214           07056        POLY2              TC       DMPSUB                                #  MULTIPLY BY X
047600,001058:    7215           00006                           EXTEND                                         
047601,001059:    7216           50117                           INDEX    POLISH                                
047602,001060:    7217           30002                           DCA      1                                     #  ADD IN NEXT COEFFICIENT
047603,001061:    7220           20155                           DAS      MPAC                                  #  USERS RESPONSIBILITY TO ASSURE NO OVFLOW
047604,001062: 
047605,001063:    7221           10140                           CCS      POLYCNT                               
047606,001064:    7222           17211                           TCF      POLYLOOP                              
047607,001065:    7223           00141                           TC       POLYRET                               #  RETURN CALLER
047608,001066: 

Page 1108

047610,001068:                                                                                                  #           MISCELLANEOUS MULTI-PRECISION ROUTINES REQUIRED IN FIXED-FIXED BUT NOT USED BY THE INTERPRETER.
047611,001069: 
047612,001070:    7224           34714        DPAGREE            CAF      ZERO                                  #  DOUBLE PRECISION ENTRY -
047613,001071:    7225           54156                           TS       MPAC       +2                         #  ZERO LOW-ORDER WORD
047614,001072: 
047615,001073:    7226           22002        TPAGREE            LXCH     Q                                     #  FORCE SIGN AGREEMENT AMONG THE TRIPLE
047616,001074:    7227           06672                           TC       BRANCH                                #  PRECISION CONTENTS OF MPAC.  RETURNING
047617,001075:    7230           17234                           TCF      ARG+                                  #  WITH SIGNUM OF THE INPUT IN A.
047618,001076:    7231           17254                           TCF      ARGZERO                               
047619,001077: 
047620,001078:    7232           44672                           CS       POSMAX                                #  IF NEGATIVE.
047621,001079:    7233           17235                           TCF      +2                                    
047622,001080: 
047623,001081:    7234           34672        ARG+               CAF      POSMAX                                
047624,001082:    7235           54002                           TS       Q                                     
047625,001083:    7236           00006                           EXTEND                                         
047626,001084:    7237           24000                           AUG      A                                     #  FORMS +-1.0.
047627,001085:    7240           60156                           AD       MPAC       +2                         
047628,001086:    7241           54156                           TS       MPAC       +2                         
047629,001087:    7242           34714                           CAF      ZERO                                  
047630,001088:    7243           60002                           AD       Q                                     
047631,001089:    7244           60155                           AD       MPAC       +1                         
047632,001090:    7245           54155                           TS       MPAC       +1                         
047633,001091:    7246           34714                           CAF      ZERO                                  
047634,001092:    7247           60002                           AD       Q                                     #  Q STILL HAS POSMAX OR NEGMAX IN IT.
047635,001093:    7250           60154                           AD       MPAC                                  
047636,001094:    7251           54154        ARGZERO2           TS       MPAC                                  #  ALWAYS SKIPPING UNLESS ARGZERO.
047637,001095:    7252           54155                           TS       MPAC       +1                         
047638,001096:    7253           00001                           TC       L                                     #  RETURN VIA L.
047639,001097: 
047640,001098:    7254           54156        ARGZERO            TS       MPAC       +2                         #  SET ALL THREE MPAC REGISTERS TO ZERO.
047641,001099:    7255           17251                           TCF      ARGZERO2                              
047642,001100: 
047643,001101:                                                                                                  #           SHORTMP MULTIPLIES THE TP CONTENTS OF MPAC BY THE SINGLE PRECISION NUMBER ARRIVING IN A.
047644,001102: 
047645,001103:    7256           54135        SHORTMP            TS       MPTEMP                                
047646,001104:    7257           00006                           EXTEND                                         
047647,001105:    7260           70156                           MP       MPAC       +2                         
047648,001106:    7261           54156                           TS       MPAC       +2                         
047649,001107:    7262           34714        SHORTMP2           CAF      ZERO                                  #  SO SUBSEQUENT DAS WILL WORK.
047650,001108:    7263           56155                           XCH      MPAC       +1                         
047651,001109:    7264           17075                           TCF      DMPSUB2                               
047652,001110: 

Page 1109

047654,001112:                                                                                                  #           DMPNSUB MULTIPLIES THE DP FRACTION ARRIVING IN MPAC BY THE SP
047655,001113:                                                                                                  #  INTEGER ARRIVING IN A.  THE DP PRODUCT DEPARTS BOTH IN MPAC AND IN
047656,001114:                                                                                                  #  A AND L.  NOTE THAT DMPNSUB NORMALLY INCREASES THE MAGNITUDE OF THE
047657,001115:                                                                                                  #  CONTENTS OF MPAC.  THE CUSTOMER MUST INSURE THAT B(A) X B(MPAC,MPAC+1)
047658,001116:                                                                                                  #  AND B(A) X B(MPAC) ARE LESS THAN 1 IN MAGNITUDE, WHERE B, AS IS OBVIOUS,
047659,001117:                                                                                                  #  INDICATES THE ARRIVING CONTENTS.
047660,001118: 
047661,001119:    7265           54135        DMPNSUB            TS       DMPNTEMP                              
047662,001120:    7266           00006                           EXTEND                                         
047663,001121:    7267           70155                           MP       MPAC       +1                         
047664,001122:    7270           52155                           DXCH     MPAC                                  #  LOW PRODUCT TO MPAC, HIGH FACTOR TO A
047665,001123:    7271           00006                           EXTEND                                         
047666,001124:    7272           70135                           MP       DMPNTEMP                              
047667,001125:    7273           30001                           CA       L                                     
047668,001126:    7274           26154                           ADS      MPAC                                  #  COMPLETING THE PRODUCT IN MPAC
047669,001127:    7275           00006                           EXTEND                                         
047670,001128:    7276           30155                           DCA      MPAC                                  #  BRINGING THE PRODUCT INTO A AND L
047671,001129:    7277           00002                           TC       Q                                     
047672,001130: 

Page 1110

047674,001132:                                                                                                  #  MISCELLANEOUS VECTOR OPERATIONS. INCLUDED HERE ARE THE FOLLOWING:
047675,001133: 
047676,001134:                                                                                                  #           1.  DOT                DP VECTOR DOT PRODUCT.
047677,001135:                                                                                                  #           2.  VXV                DP VECTOR CROSS PRODUCT.
047678,001136:                                                                                                  #           3.  VXSC               DP VECTOR TIMES SCALAR.
047679,001137:                                                                                                  #           4.  V/SC               DP VECTOR DIVIDED BY SCALAR.
047680,001138:                                                                                                  #           5.  VPROJ              DP VECTOR PROJECTION. ( (MPAC.X)MPAC ).
047681,001139:                                                                                                  #           6.  VXM                DP VECTOR POST-MULTIPLIED BY MATRIX.
047682,001140:                                                                                                  #           7.  MXV                DP VECTOR PRE-MULTIPLIED BY MATRIX.
047683,001141: 
047684,001142:    7300           07123        DOT                TC       PREDOT                                #  DO THE DOT PRODUCT AND EXIT, CHANGING
047685,001143:    7301           34714        DMODE              CAF      ZERO                                  #  THE MODE TO DP SCALAR.
047686,001144:    7302           16027                           TCF      NEWMODE                               
047687,001145: 
047688,001146: 
047689,001147:    7303           34711        MXV                CAF      TWO                                   #  SET UP MATINC AND DOTINC FOR ROW
047690,001148:    7304           54140                           TS       MATINC                                #  VECTORS.
047691,001149:    7305           17311                           TCF      VXM/MXV                               #  GO TO COMMON PORTION.
047692,001150: 
047693,001151:    7306           44377        VXM                CS       TEN                                   #  SET MATINC AND DOTINC TO REFER TO MATRIX
047694,001152:    7307           54140                           TS       MATINC                                #  AS THREE COLUMN VECTORS.
047695,001153:    7310           36211                           CAF      SIX                                   
047696,001154: 

Page 1111

047698,001156:                                                                                                  #           COMMON PORTION OF MXV AND VXM.
047699,001157: 
047700,001158:    7311           54136        VXM/MXV            TS       DOTINC                                
047701,001159:                                                                                                  #           ITRACE (2) REFERS TO "VXM/MXV".
047702,001160:    7312           07501                           TC       MPACVBUF                              #  SAVE VECTOR IN MPAC FOR FURTHER USE.
047703,001161: 
047704,001162:    7313           07125                           TC       DOTSUB                                #  GO DOT TO GET X COMPONENT OF ANSWER.
047705,001163:    7314           00006                           EXTEND                                         
047706,001164:    7315           30123                           DCA      VBUF                                  #  MOVE MPAC VECTOR BACK INTO MPAC, SAVING
047707,001165:    7316           52155                           DXCH     MPAC                                  #  NEW X COMPONENT IN BUF2.
047708,001166:    7317           52134                           DXCH     BUF2                                  
047709,001167:    7320           00006                           EXTEND                                         
047710,001168:    7321           30125                           DCA      VBUF       +2                         
047711,001169:    7322           52160                           DXCH     MPAC       +3                         
047712,001170:    7323           00006                           EXTEND                                         
047713,001171:    7324           30127                           DCA      VBUF       +4                         
047714,001172:    7325           52162                           DXCH     MPAC       +5                         
047715,001173:    7326           30140                           CA       MATINC                                #  INITIALIZE ADDRWD FOR NEXT DOT PRODUCT.
047716,001174:    7327           26116                           ADS      ADDRWD                                #  FORMS BASE ADDRESS OF NEXT COLUMN(ROW).
047717,001175: 
047718,001176:    7330           07125                           TC       DOTSUB                                
047719,001177:    7331           52123                           DXCH     VBUF                                  #  MOVE GIVEN VECTOR BACK TO MPAC, SAVING Y
047720,001178:    7332           52155                           DXCH     MPAC                                  #  COMPONENT OF ANSWER IN VBUF +2.
047721,001179:    7333           52125                           DXCH     VBUF       +2                         
047722,001180:    7334           52160                           DXCH     MPAC       +3                         
047723,001181:    7335           52127                           DXCH     VBUF       +4                         
047724,001182:    7336           52162                           DXCH     MPAC       +5                         
047725,001183:    7337           30140                           CA       MATINC                                #  FORM ADDRESS OF LAST COLUMN OR ROW.
047726,001184:    7340           26116                           ADS      ADDRWD                                
047727,001185: 
047728,001186:    7341           07125                           TC       DOTSUB                                
047729,001187:    7342           52134                           DXCH     BUF2                                  #  ANSWER NOW COMPLETE. PUT COMPONENTS INTO
047730,001188:    7343           52155                           DXCH     MPAC                                  #  PROPER MPAC REGISTERS.
047731,001189:    7344           52162                           DXCH     MPAC       +5                         
047732,001190:    7345           52125                           DXCH     VBUF       +2                         
047733,001191:    7346           52160                           DXCH     MPAC       +3                         
047734,001192:    7347           16030                           TCF      DANZIG                                #  EXIT.
047735,001193: 

Page 1112

047737,001195:                                                                                                  #           VXSC - VECTOR TIMES SCALAR.
047738,001196: 
047739,001197:    7350           10163        VXSC               CCS      MODE                                  #  TEST PRESENT MODE.
047740,001198:    7351           17377                           TCF      DVXSC                                 #  SEPARATE ROUTINE WHEN SCALAR IS IN MPAC.
047741,001199:    7352           17377                           TCF      DVXSC                                 
047742,001200: 
047743,001201:    7353           07056        VVXSC              TC       DMPSUB                                #  COMPUTE X COMPONENT
047744,001202:    7354           07107                           TC       VROUND                                #  AND ROUND IT.
047745,001203:    7355           52160                           DXCH     MPAC       +3                         #  PUT Y COMPONENT INTO MPAC SAVING MPAC IN
047746,001204:    7356           52155                           DXCH     MPAC                                  #  MPAC +3.
047747,001205:    7357           52160                           DXCH     MPAC       +3                         
047748,001206: 
047749,001207:    7360           07056                           TC       DMPSUB                                #  DO SAME FOR Y AND Z COMPONENTS.
047750,001208:    7361           07107                           TC       VROUND                                
047751,001209:    7362           52162                           DXCH     MPAC       +5                         
047752,001210:    7363           52155                           DXCH     MPAC                                  
047753,001211:    7364           52162                           DXCH     MPAC       +5                         
047754,001212: 
047755,001213:    7365           07056                           TC       DMPSUB                                
047756,001214:    7366           07107                           TC       VROUND                                
047757,001215:    7367           52155        VROTATEX           DXCH     MPAC                                  #  EXIT USED TO RESTORE MPAC AFTER THIS
047758,001216:    7370           52162                           DXCH     MPAC       +5                         #  TYPE OF ROTATION. CALLED BY VECTOR SHIFT
047759,001217:    7371           52160                           DXCH     MPAC       +3                         #  RIGHT, V/SC, ETC.
047760,001218:    7372           52155                           DXCH     MPAC                                  
047761,001219:    7373           16030                           TCF      DANZIG                                
047762,001220: 

Page 1113

047764,001222:                                                                                                  #           DP VECTOR PROJECTION ROUTINE.
047765,001223: 
047766,001224:    7374           07123        VPROJ              TC       PREDOT                                #  (MPAC.X)MPAC IS COMPUTED AND LEFT IN
047767,001225:    7375           44710                           CS       FOUR                                  #  MPAC. DO DOT AND FALL INTO DVXSC.
047768,001226:    7376           26116                           ADS      ADDRWD                                
047769,001227: 
047770,001228:                                                                                                  #           VXSC WHEN SCALAR ARRIVES IN MPAC AND VECTOR IS AT X.
047771,001229: 
047772,001230:    7377           00006        DVXSC              EXTEND                                         #  SAVE SCALAR IN MPAC +3 AND GET X
047773,001231:    7400           30155                           DCA      MPAC                                  #  COMPONENT OF ANSWER.
047774,001232:    7401           52160                           DXCH     MPAC       +3                         
047775,001233:    7402           07056                           TC       DMPSUB                                
047776,001234:    7403           07107                           TC       VROUND                                
047777,001235: 
047778,001236:    7404           34711                           CAF      TWO                                   #  ADVANCE ADDRWD TO Y COMPONENT OF X.
047779,001237:    7405           26116                           ADS      ADDRWD                                
047780,001238:    7406           00006                           EXTEND                                         
047781,001239:    7407           30160                           DCA      MPAC       +3                         #  PUT SCALAR BACK INTO MPAC AND SAVE
047782,001240:    7410           52155                           DXCH     MPAC                                  #  X RESULT IN MPAC +5.
047783,001241:    7411           52162                           DXCH     MPAC       +5                         
047784,001242:    7412           07056                           TC       DMPSUB                                
047785,001243:    7413           07107                           TC       VROUND                                
047786,001244: 
047787,001245:    7414           34711                           CAF      TWO                                   
047788,001246:    7415           26116                           ADS      ADDRWD                                #  TO Z COMPONENT.
047789,001247:    7416           52160                           DXCH     MPAC       +3                         #  BRING SCALAR BACK, PUTTING Y RESULT IN
047790,001248:    7417           52155                           DXCH     MPAC                                  #  THE PROPER PLACE.
047791,001249:    7420           52160                           DXCH     MPAC       +3                         
047792,001250:    7421           07056                           TC       DMPSUB                                
047793,001251:    7422           07107                           TC       VROUND                                
047794,001252: 
047795,001253:    7423           52155                           DXCH     MPAC                                  #  PUT Z COMPONENT IN PROPER PLACE, ALSO
047796,001254:    7424           52162                           DXCH     MPAC       +5                         #  POSITIONING X.
047797,001255:    7425           52155                           DXCH     MPAC                                  
047798,001256: 
047799,001257:    7426           16470                           TCF      VMODE                                 #  MODE HAS CHANGED TO VECTOR.
047800,001258: 

Page 1114

047802,001260:                                                                                                  #           THE VECTOR CROSS PRODUCT ROUTINE CALCULATES (X M -X M ,X M -X M ,X M -X M ) WHERE M IS THE VECTOR IN
047803,001261:                                                                                                  #                                                         3 2  2 3  1 3  3 1  2 1  1 2
047804,001262:                                                                                                  #  MPAC AND X THE VECTOR AT THE GIVEN ADDRESS.
047805,001263: 
047806,001264: 
047807,001265:    7427           00006        VXV                EXTEND                                         
047808,001266:    7430           30162                           DCA      MPAC       +5                         #  FORM UP M3X1, LEAVING M1 IN VBUF.
047809,001267:    7431           52155                           DXCH     MPAC                                  
047810,001268:    7432           52123                           DXCH     VBUF                                  
047811,001269:    7433           07056                           TC       DMPSUB                                #  BY X1.
047812,001270: 
047813,001271:    7434           00006                           EXTEND                                         
047814,001272:    7435           40160                           DCS      MPAC       +3                         #  CALCULATE -X1M2, SAVING X1M3 IN VBUF +2.
047815,001273:    7436           52155                           DXCH     MPAC                                  
047816,001274:    7437           52125                           DXCH     VBUF       +2                         
047817,001275:    7440           07056                           TC       DMPSUB                                
047818,001276: 
047819,001277:    7441           34711                           CAF      TWO                                   #  ADVANCE ADDRWD TO X2.
047820,001278:    7442           26116                           ADS      ADDRWD                                
047821,001279:    7443           00006                           EXTEND                                         
047822,001280:    7444           40162                           DCS      MPAC       +5                         #  PREPARE TO GET -X2M3, SAVING -X1M2 IN
047823,001281:    7445           52155                           DXCH     MPAC                                  #  MPAC +5.
047824,001282:    7446           52162                           DXCH     MPAC       +5                         
047825,001283:    7447           07056                           TC       DMPSUB                                
047826,001284: 
047827,001285:    7450           00006                           EXTEND                                         
047828,001286:    7451           30123                           DCA      VBUF                                  #  GET X2M1, SAVING -X2M3 IN VBUF +4.
047829,001287:    7452           52155                           DXCH     MPAC                                  
047830,001288:    7453           52127                           DXCH     VBUF       +4                         
047831,001289:    7454           07056                           TC       DMPSUB                                
047832,001290: 
047833,001291:    7455           34711                           CAF      TWO                                   #  ADVANCE ADDRWD TO X3.
047834,001292:    7456           26116                           ADS      ADDRWD                                
047835,001293:    7457           00006                           EXTEND                                         
047836,001294:    7460           40123                           DCS      VBUF                                  #  GET -X3M1, ADDING X2M1 TO MPAC +5 TO
047837,001295:    7461           52155                           DXCH     MPAC                                  #  COMPLETE THE Z COMPONENT OF THE ANSWER.
047838,001296:    7462           20162                           DAS      MPAC       +5                         
047839,001297: 
047840,001298:    7463           00006                           EXTEND                                         
047841,001299:    7464           17466                           BZF      +2                                    
047842,001300:    7465           06760                           TC       OVERFLWZ                              
047843,001301: 
047844,001302:    7466           07056                           TC       DMPSUB                                
047845,001303:    7467           52125                           DXCH     VBUF       +2                         #  MOVE X1M3 TO MPAC +3 SETTING UP FOR X3M2
047846,001304:    7470           52160                           DXCH     MPAC       +3                         #  AND ADD -X3M1 TO MPAC +3 TO COMPLETE THE
047847,001305:    7471           52155                           DXCH     MPAC                                  #  Y COMPONENT OF THE RESULT.
047848,001306:    7472           20160                           DAS      MPAC       +3                         
047849,001307: 
047850,001308:    7473           00006                           EXTEND                                         
047851,001309:    7474           17476                           BZF      +2                                    

Page 1115

047853,001311:    7475           06763                           TC       OVERFLWY                              
047854,001312: 
047855,001313:    7476           07056                           TC       DMPSUB                                
047856,001314:    7477           52127                           DXCH     VBUF       +4                         #  GO ADD -X2M3 TO X3M2 TO COMPLETE THE X
047857,001315:    7500           16747                           TCF      ENDVXV                                #  COMPONENT (TAIL END OF DAD).
047858,001316: 
047859,001317:                                                                                                  #           THE MPACVBUF SUBROUTINE SAVES THE VECTOR IN MPAC IN VBUF WITHOUT CLOBBERING MPAC.
047860,001318: 
047861,001319:    7501           00006        MPACVBUF           EXTEND                                         #  CALLED BY MXV, VXM, AND UNIT.
047862,001320:    7502           30155                           DCA      MPAC                                  
047863,001321:    7503           52123                           DXCH     VBUF                                  
047864,001322:    7504           00006                           EXTEND                                         
047865,001323:    7505           30160                           DCA      MPAC       +3                         
047866,001324:    7506           52125                           DXCH     VBUF       +2                         
047867,001325:    7507           00006                           EXTEND                                         
047868,001326:    7510           30162                           DCA      MPAC       +5                         
047869,001327:    7511           52127                           DXCH     VBUF       +4                         
047870,001328:    7512           00002                           TC       Q                                     #  RETURN TO CALLER.
047871,001329: 
047872,001330: 
047873,001331:                                                                                                  #           DOUBLE PRECISION SIGN AGREE ROUTINE. ARRIVE WITH INPUT IN A+L. OUTPUT IS IN A + L.
047874,001332: 
047875,001333:    7513           10000        ALSIGNAG           CCS      A                                     #  TEST UPPER PART.
047876,001334:    7514           17520                           TCF      UPPOS                                 #  IT IS POSITIVE
047877,001335:    7515           00002                           TC       Q                                     #  ZERO
047878,001336:    7516           17530                           TCF      UPNEG                                 #  NEGATIVE
047879,001337:    7517           00002                           TC       Q                                     #  ZERO
047880,001338: 
047881,001339:    7520           56001        UPPOS              XCH      L                                     #  SAVE DECREMENTED UPPER PART.
047882,001340:    7521           64675                           AD       HALF                                  
047883,001341:    7522           64675                           AD       HALF                                  
047884,001342:    7523           54000                           TS       A                                     #  SKIPS ON OVERFLOW
047885,001343:    7524           17526                           TCF      +2                                    
047886,001344:    7525           24001                           INCR     L                                     #  RESTORE UPPER TO ROIGINAL VALUE
047887,001345:    7526           56001                           XCH      L                                     #  SWAP A + L BACK.
047888,001346:    7527           00002                           TC       Q                                     
047889,001347: 
047890,001348:    7530           56001        UPNEG              XCH      L                                     #  SAVE COMPLEMENTED + DECREMENTED UPPER PT
047891,001349:    7531           64674                           AD       NEGMAX                                
047892,001350:    7532           67716                           AD       NEGONE                                
047893,001351:    7533           54000                           TS       A                                     
047894,001352:    7534           17536                           TCF      +2                                    #  DONT INCREMENT IF NO OVERFLOW.
047895,001353:    7535           24001                           INCR     L                                     
047896,001354:    7536           56001                           XCH      L                                     
047897,001355:    7537           40000                           COM                                            #  MAKE NEGATIVE AGAIN.
047898,001356:    7540           00002                           TC       Q                                     
047899,001357: 

Page 1116

047901,001359:                                                                                                  #           INTERPRETIVE INSTRUCTIONS WHOSE EXECUTION CONSISTS OF PRINCIPALLY CALLING SUBROUTINES.
047902,001360: 
047903,001361:    7541           07056        DMP1               TC       DMPSUB                                #  DMP INSTRUCTION.
047904,001362:    7542           16030                           TCF      DANZIG                                
047905,001363: 
047906,001364:    7543           07056        DMPR               TC       DMPSUB                                
047907,001365:    7544           07106                           TC       ROUNDSUB   +1                         #  (C(A) = +0).
047908,001366:    7545           16030                           TCF      DANZIG                                
047909,001367: 
047910,001368:    7546           00006        DDV                EXTEND                                         
047911,001369:    7547           50116                           INDEX    ADDRWD                                #  MOVE DIVIDEND INTO BUF.
047912,001370:    7550           30001                           DCA      0                                     
047913,001371:    7551           17556                           TCF      BDDV       +4                         
047914,001372: 
047915,001373:    7552           00006        BDDV               EXTEND                                         #  MOVE DIVISOR INTO MPAC SAVING MPAC, THE
047916,001374:    7553           50116                           INDEX    ADDRWD                                #  DIVIDEND, IN BUF.
047917,001375:    7554           30001                           DCA      0                                     
047918,001376:    7555           52155                           DXCH     MPAC                                  
047919,001377:    7556           52131                 +4        DXCH     BUF                                   
047920,001378:    7557           34714                           CAF      ZERO                                  #  DIVIDE ROUTINES IN BANK 0.
047921,001379:    7560           54004                           TS       FBANK                                 
047922,001380:    7561           12353                           TCF      DDV/BDDV                              
047923,001381: 
047924,001382:    7562           30116        SETPD              CA       ADDRWD                                #  MUST SET TO WORK AREA, OR EBANK TROUBLE.
047925,001383:    7563           54166                           TS       PUSHLOC                               
047926,001384:    7564           16032                           TCF      NOIBNKSW                              #  NO FBANK SWITCH REQUIRED.
047927,001385: 
047928,001386:    7565           34714        TSLC               CAF      ZERO                                  #  SHIFTING ROUTINES LOCATED IN BANK 00.
047929,001387:    7566           54004                           TS       FBANK                                 
047930,001388:    7567           12172                           TCF      TSLC2                                 
047931,001389: 
047932,001390:    7570           36043        GSHIFT             CAF      LOW7                                  #  USED AS MASK AT GENSHIFT. THIS PROCESSES
047933,001391:    7571           54004                           TS       FBANK                                 #  ANY SHIFT INSTRUCTION (EXCEPT TSLC) WITH
047934,001392:    7572           12214                           TCF      GENSHIFT                              #  AN ADDRESS (ROUTINES IN BANK 0).
047935,001393: 

Page 1117

047937,001395:                                                                                                  #           THE FOLLOWING IS THE PROLOGUE TO V/SC. IF THE PRESENT MODE IS VECTOR, IT SAVES THE SCALAR AT X IN BUF
047938,001396:                                                                                                  #  AND CALLS THE V/SC ROUTINE IN BANK 0. IF THE PRESENT MODE IS SCALAR, IT MOVES THE VECTOR AT X INTO MPAC, SAVING
047939,001397:                                                                                                  #  THE SCALAR IN MPAC IN BUF BEFORE CALLING THE V/SC ROUTINE IN BANK 0.
047940,001398: 
047941,001399: 
047942,001400:    7573           10163        V/SC               CCS      MODE                                  
047943,001401:    7574           17605                           TCF      DV/SC                                 #  MOVE VECTOR INTO MPAC.
047944,001402:    7575           17605                           TCF      DV/SC                                 
047945,001403: 
047946,001404:    7576           00006        VV/SC              EXTEND                                         
047947,001405:    7577           50116                           INDEX    ADDRWD                                
047948,001406:    7600           30001                           DCA      0                                     
047949,001407:    7601           52131        V/SC1              DXCH     BUF                                   #  IN BOTH CASES, VECTOR IS NOW IN MPAC AND
047950,001408:    7602           34714                           CAF      ZERO                                  #  SCALAR IN BUF.
047951,001409:    7603           54004                           TS       FBANK                                 
047952,001410:    7604           12654                           TCF      V/SC2                                 
047953,001411: 
047954,001412:    7605           00006        DV/SC              EXTEND                                         
047955,001413:    7606           50116                           INDEX    ADDRWD                                
047956,001414:    7607           30003                           DCA      2                                     
047957,001415:    7610           52160                           DXCH     MPAC       +3                         
047958,001416:    7611           00006                           EXTEND                                         
047959,001417:    7612           50116                           INDEX    ADDRWD                                
047960,001418:    7613           30005                           DCA      4                                     
047961,001419:    7614           52162                           DXCH     MPAC       +5                         
047962,001420: 
047963,001421:    7615           44712                           CS       ONE                                   #  CHANGE MODE TO VECTOR.
047964,001422:    7616           54163                           TS       MODE                                  
047965,001423: 
047966,001424:    7617           00006                           EXTEND                                         
047967,001425:    7620           50116                           INDEX    ADDRWD                                
047968,001426:    7621           30001                           DCA      0                                     
047969,001427:    7622           52155                           DXCH     MPAC                                  
047970,001428:    7623           17601                           TCF      V/SC1                                 #  FINISH PROLOGUE AT COMMON SECTION.
047971,001429: 

Page 1118

047973,001431:                                                                                                  #           SIGN AND COMPLEMENT INSTRUCTIONS.
047974,001432: 
047975,001433:    7624           50116        SIGN               INDEX    ADDRWD                                #  CALL COMP INSTRUCTION IF WORD AT X IS
047976,001434:    7625           10000                           CCS      0                                     #  NEGATIVE NON-ZERO.
047977,001435:    7626           16030                           TCF      DANZIG                                
047978,001436:    7627           17631                           TCF      +2                                    
047979,001437:    7630           17637                           TCF      COMP                                  #  DO THE COMPLEMENT.
047980,001438: 
047981,001439:    7631           50116                           INDEX    ADDRWD                                
047982,001440:    7632           10001        CCSL               CCS      1                                     
047983,001441:    7633           16030                           TCF      DANZIG                                
047984,001442:    7634           16030                           TCF      DANZIG                                
047985,001443:    7635           17637                           TCF      COMP                                  
047986,001444:    7636           16030                           TCF      DANZIG                                
047987,001445:    7637           00006        COMP               EXTEND                                         #  COMPLEMENT DP MPAC IN EVERY CASE.
047988,001446:    7640           40155                           DCS      MPAC                                  
047989,001447:    7641           52155                           DXCH     MPAC                                  
047990,001448: 
047991,001449:    7642           10163                           CCS      MODE                                  #  EITHER COMPLEMENT MPAC +3 OR THE REST OF
047992,001450:    7643           17654                           TCF      DCOMP                                 #  THE VECTOR ACCUMULATOR.
047993,001451:    7644           17654                           TCF      DCOMP                                 
047994,001452: 
047995,001453:    7645           00006                           EXTEND                                         #  VECTOR COMPLEMENT.
047996,001454:    7646           40160                           DCS      MPAC       +3                         
047997,001455:    7647           52160                           DXCH     MPAC       +3                         
047998,001456:    7650           00006                           EXTEND                                         
047999,001457:    7651           40162                           DCS      MPAC       +5                         
048000,001458:    7652           52162                           DXCH     MPAC       +5                         
048001,001459:    7653           16030                           TCF      DANZIG                                
048002,001460: 
048003,001461:    7654           40156        DCOMP              CS       MPAC       +2                         
048004,001462:    7655           54156                           TS       MPAC       +2                         
048005,001463:    7656           16030                           TCF      DANZIG                                
048006,001464: 

Page 1119

048008,001466:                                                                                                  #           THE FOLLOWING SHORT SHIFT CODES REQUIRE NO ADDRESS WORD:
048009,001467: 
048010,001468:                                                                                                  #           1.  SR1 TO SR4         SCALAR SHIFT RIGHT.
048011,001469:                                                                                                  #           2.  SR1R TO SR4R       SCALAR SHIFT RIGHT AND ROUND.
048012,001470:                                                                                                  #           3.  SL1 TO SL4         SCALAR SHIFT LEFT.
048013,001471:                                                                                                  #           4.  SL1R TO SL4R       SCALAR SHIFT LEFT AND ROUND.
048014,001472: 
048015,001473:                                                                                                  #           5.  VSR1 TO VSR8       VECTOR SHIFT RIGHT (ALWAYS ROUNDS).
048016,001474:                                                                                                  #           6.  VSL1 TO VSL8       VECTOR SHIFT LEFT (NEVER ROUNDS).
048017,001475: 
048018,001476:                                                                                                  #           THE FOLLOWING CODES REQUIRE AN ADDRESS WHICH MAY BE INDEXED:*
048019,001477: 
048020,001478:                                                                                                  #           1.  SR                 SCALAR SHIFT RIGHT.
048021,001479:                                                                                                  #           2.  SRR                SCALAR SHIFT RIGHT AND ROUND.
048022,001480:                                                                                                  #           3.  SL                 SCALAR SHIFT LEFT.
048023,001481:                                                                                                  #           4.  SLR                SCALAR SHIFT LEFT AND ROUND.
048024,001482: 
048025,001483:                                                                                                  #           5.  VSR                VECTOR SHIFT RIGHT.
048026,001484:                                                                                                  #           6.  VSL                VECTOR SHIFT LEFT.
048027,001485: 
048028,001486:                                                                                                  #  *  IF THE ADDRESS IS INDEXED, AND THE INDEX MODIFICATION RESULTS IN A NEGATIVE SHIFT COUNT, A SHIFT OF THE
048029,001487:                                                                                                  #  ABSOLUTE VALUE OF THE COUNT IS DONE IN THE OPPOSITE DIRECTION.
048030,001488: 
048031,001489: 
048032,001490: 00,2017                                           BANK     00                                    
048033,001491: 
048034,001492: 00,2017                                           COUNT    00/INTER                              
048035,001493: 
048036,001494: 00,2017           36211        SHORTT             CAF      SIX                                   #  SCALAR SHORT SHIFTS COME HERE. THE SHIFT
048037,001495: 00,2020           70020                           MASK     CYR                                   #  COUNT-1 IS NOW IN BITS 2-3 OF CYR. THE
048038,001496: 00,2021           54021                           TS       SR                                    #  ROUNDING BIT IS IN BIT1 AT THIS POINT.
048039,001497: 
048040,001498: 00,2022           10020                           CCS      CYR                                   #  SEE IF RIGHT OR LEFT SHIFT DESIRED.
048041,001499: 00,2023           12101                           TCF      TSSL                                  #  SHIFT LEFT.
048042,001500: 
048043,001501: 00,2024           00024        SRDDV              DEC      20         B-14                       #  MPTEMP SETTING FOR SR BEFORE DDV.
048044,001502: 
048045,001503: 00,2025           50021        TSSR               INDEX    SR                                    #  GET SHIFTING BIT.
048046,001504: 00,2026           34675                           CAF      BIT14                                 
048047,001505: 00,2027           54135                           TS       MPTEMP                                
048048,001506: 
048049,001507: 00,2030           10020                           CCS      CYR                                   #  SEE IF A ROUND IS DESIRED.
048050,001508: 00,2031           02050        RIGHTR             TC       MPACSRND                              #  YES - SHIFT RIGHT AND ROUND.
048051,001509: 00,2032           16027                           TCF      NEWMODE                               #  SET MODE TO DP (C(A) = 0).
048052,001510: 00,2033           30135        MPACSHR            CA       MPTEMP                                #  DO A TRIPLE PRECISION SHIFT RIGHT.
048053,001511: 00,2034           00006                           EXTEND                                         
048054,001512: 00,2035           70156                           MP       MPAC       +2                         
048055,001513: 00,2036           54156                 +3        TS       MPAC       +2                         #  (EXIT FROM SQRT AND ABVAL).
048056,001514: 00,2037           30135                           CA       MPTEMP                                
048057,001515: 00,2040           00006                           EXTEND                                         

Page 1120

048059,001517: 00,2041           70154                           MP       MPAC                                  #  SHIFT MAJOR PART INTO A,L AND PLACE IN
048060,001518: 00,2042           52155                           DXCH     MPAC                                  #  MPAC,+1.
048061,001519: 00,2043           30135                           CA       MPTEMP                                
048062,001520: 00,2044           00006                           EXTEND                                         
048063,001521: 00,2045           70001                           MP       L                                     #  ORIGINAL C(MPAC +1).
048064,001522: 00,2046           20156                           DAS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
048065,001523: 00,2047           16030                           TCF      DANZIG                                
048066,001524: 
048067,001525:                                                                                                  #           MPAC SHIFT RIGHT AND ROUND SUBROUTINES.
048068,001526: 
048069,001527: 00,2050           30156        MPACSRND           CA       MPAC       +2                         #  WE HAVE TO DO ALL THREE MULTIPLIES SINCE
048070,001528: 00,2051           00006                           EXTEND                                         #  MPAC +1 AND MPAC +2 MIGHT HAVE SIGN
048071,001529: 00,2052           70135                           MP       MPTEMP                                #  DISAGREEMENT WITH A SHIFT RIGHT OF 1.
048072,001530: 00,2053           56155                           XCH      MPAC       +1                         
048073,001531: 00,2054           00006                           EXTEND                                         
048074,001532: 00,2055           70135                           MP       MPTEMP                                
048075,001533: 00,2056           56155                           XCH      MPAC       +1                         #  TRIAL MINOR PART.
048076,001534: 00,2057           60001                           AD       L                                     
048077,001535: 
048078,001536: 00,2060           60000        VSHR2              DOUBLE                                         #  (FINISH VECTOR COMPONENT SHIFT RIGHT
048079,001537: 00,2061           54156                           TS       MPAC       +2                         #  AND ROUND.
048080,001538: 00,2062           12064                           TCF      +2                                    
048081,001539: 00,2063           26155                           ADS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
048082,001540: 
048083,001541: 00,2064           34714                           CAF      ZERO                                  
048084,001542: 00,2065           54156                           TS       MPAC       +2                         
048085,001543: 00,2066           56154                           XCH      MPAC                                  #  SETTING TO ZERO SO FOLLOWING DAS WORKS.
048086,001544: 00,2067           00006                           EXTEND                                         
048087,001545: 00,2070           70135                           MP       MPTEMP                                
048088,001546: 00,2071           20155                           DAS      MPAC                                  #  AGAIN NO OVERFLOW.
048089,001547: 00,2072           00002                           TC       Q                                     
048090,001548: 
048091,001549: 00,2073           30135        VSHRRND            CA       MPTEMP                                #  ENTRY TO SHIFT RIGHT AND ROUND MPAC WHEN
048092,001550: 00,2074           00006                           EXTEND                                         #  MPAC CONTAINS A VECTOR COMPONENT.
048093,001551: 00,2075           70155                           MP       MPAC       +1                         
048094,001552: 00,2076           54155                           TS       MPAC       +1                         
048095,001553: 00,2077           56001                           XCH      L                                     
048096,001554: 00,2100           12060                           TCF      VSHR2                                 #  GO ADD ONE IF NECESSARY AND FINISH.
048097,001555: 

Page 1121

048099,001557:                                                                                                  #           ROUTINE FOR SHORT SCALAR SHIFT LEFT (AND MAYBE ROUND).
048100,001558: 
048101,001559: 00,2101           30021        TSSL               CA       SR                                    #  GET SHIFT COUNT FOR SR.
048102,001560: 00,2102           54135                 +1        TS       MPTEMP                                
048103,001561: 
048104,001562: 00,2103           00006                 +2        EXTEND                                         #  ENTRY HERE FROM SL FOR SCALARS.
048105,001563: 00,2104           30156                           DCA      MPAC       +1                         #  SHIFTING LEFT ONE PLACE AT A TIME IS
048106,001564: 00,2105           20156                           DAS      MPAC       +1                         #  FASTER THAN DOING THE WHOLE SHIFT WITH
048107,001565: 00,2106           60154                           AD       MPAC                                  #  MULTIPLIES ASSUMING THAT FREQUENCY OF
048108,001566: 00,2107           60154                           AD       MPAC                                  #  SHIFT COUNTS GOES DOWN RAPIDLY AS A
048109,001567: 00,2110           54154                           TS       MPAC                                  #  FUNCTION OF THEIR MAGNITUDE.
048110,001568: 00,2111           12113                           TCF      +2                                    
048111,001569: 00,2112           54121                           TS       OVFIND                                #  OVERFLOW. (LEAVES OVERFLOW-CORRECTED
048112,001570:                                                                                                  #                                          RESULT ANYWAY).
048113,001571: 00,2113           10135                           CCS      MPTEMP                                #  LOOP ON DECREMENTED SHIFT COUNT.
048114,001572: 00,2114           12102                           TCF      TSSL       +1                         
048115,001573: 
048116,001574: 00,2115           10020                           CCS      CYR                                   #  SEE IF ROUND WANTED.
048117,001575: 00,2116           07105        ROUND              TC       ROUNDSUB                              #  YES - ROUND AND EXIT.
048118,001576: 00,2117           16030                           TCF      DANZIG                                #  SL LEAVES A ZERO IN CYR FOR NO ROUND.
048119,001577: 00,2120           16030                           TCF      DANZIG                                #  NO - EXIT IMMEDIATL
048120,001578: 

Page 1122

048122,001580:                                                                                                  #  VECTOR SHIFTING ROUTINES.
048123,001581: 
048124,001582: 00,2121           34716        SHORTV             CAF      LOW3                                  #  SAVE 3 BIT SHIFT COUNT - 1 WITHOUT
048125,001583: 00,2122           70020                           MASK     CYR                                   #  EDITING CYR.
048126,001584: 00,2123           54135                           TS       MPTEMP                                
048127,001585: 00,2124           10020                           CCS      CYR                                   #  SEE IF LEFT OR RIGHT SHIFT.
048128,001586: 00,2125           12145                           TCF      VSSL                                  #  VECTOR SHIFT LEFT.
048129,001587: 00,2126           00176        OCT176             OCT      176                                   #  USED IN PROCESSED SHIFTS WITH - COUNT.
048130,001588: 
048131,001589: 00,2127           50135        VSSR               INDEX    MPTEMP                                #  (ENTRY FROM SR). PICK UP SHIFTING BIT.
048132,001590: 00,2130           34675                           CAF      BIT14                                 #  MPTEMP CONTAINS THE SHIFT COUNT - 1.
048133,001591: 00,2131           54135                           TS       MPTEMP                                
048134,001592: 00,2132           02073                           TC       VSHRRND                               #  SHIFT X COMPONENT.
048135,001593: 
048136,001594: 00,2133           52155                           DXCH     MPAC                                  #  SWAP X AND Y COMPONENTS.
048137,001595: 00,2134           52160                           DXCH     MPAC       +3                         
048138,001596: 00,2135           52155                           DXCH     MPAC                                  
048139,001597: 00,2136           02073                           TC       VSHRRND                               #  SHIFT Y COMPONENT.
048140,001598: 
048141,001599: 00,2137           52155                           DXCH     MPAC                                  #  SWAP Y AND Z COMPONENTS.
048142,001600: 00,2140           52162                           DXCH     MPAC       +5                         
048143,001601: 00,2141           52155                           DXCH     MPAC                                  
048144,001602: 00,2142           02073                           TC       VSHRRND                               #  SHIFT Z COMPONENT.
048145,001603: 
048146,001604: 00,2143           17367                           TCF      VROTATEX                              #  RESTORE COMPONENTS TO PROPER PLACES.
048147,001605: 

Page 1123

048149,001607:                                                                                                  #  VECTOR SHIFT LEFT - DONE ONE PLACE AT A TIME.
048150,001608: 
048151,001609: 00,2144           54135                 -1        TS       MPTEMP                                #  SHIFTING LOOP.
048152,001610: 
048153,001611: 00,2145           00006        VSSL               EXTEND                                         
048154,001612: 00,2146           30155                           DCA      MPAC                                  
048155,001613: 00,2147           20155                           DAS      MPAC                                  
048156,001614: 00,2150           00006                           EXTEND                                         
048157,001615: 00,2151           12153                           BZF      +2                                    
048158,001616: 00,2152           06766                           TC       OVERFLOW                              
048159,001617: 
048160,001618: 00,2153           00006                           EXTEND                                         
048161,001619: 00,2154           30160                           DCA      MPAC       +3                         
048162,001620: 00,2155           20160                           DAS      MPAC       +3                         
048163,001621: 00,2156           00006                           EXTEND                                         
048164,001622: 00,2157           12161                           BZF      +2                                    
048165,001623: 00,2160           06763                           TC       OVERFLWY                              
048166,001624: 
048167,001625: 00,2161           00006                           EXTEND                                         
048168,001626: 00,2162           30162                           DCA      MPAC       +5                         
048169,001627: 00,2163           20162                           DAS      MPAC       +5                         
048170,001628: 00,2164           00006                           EXTEND                                         
048171,001629: 00,2165           12167                           BZF      +2                                    
048172,001630: 00,2166           06760                           TC       OVERFLWZ                              
048173,001631: 
048174,001632: 00,2167           10135                           CCS      MPTEMP                                #  LOOP ON DECREMENTED SHIFT COUNTER.
048175,001633: 00,2170           12144                           TCF      VSSL       -1                         
048176,001634: 00,2171           16030                           TCF      DANZIG                                #  EXIT.
048177,001635: 

Page 1124

048179,001637:                                                                                                  #           TSLC - TRIPLE SHIFT LEFT AND COUNT. SHIFTS MPAC LEFT UNTIL GREATER THAN .5 IN MAGNITUDE, LEAVING
048180,001638:                                                                                                  #  THE COMPLEMENT OF THE NUMBER OF SHIFTS REQUIRED IN X.
048181,001639: 
048182,001640: 00,2172           54135        TSLC2              TS       MPTEMP                                #  START BY ZEROING SHIFT COUNT (IN A NOW).
048183,001641: 00,2173           06672                           TC       BRANCH                                #  EXIT WITH NO SHIFTING IF ARGUMENT ZERO.
048184,001642: 00,2174           12176                           TCF      +2                                    
048185,001643: 00,2175           12212                           TCF      ENDTSLC                               #  STORES ZERO SHIFT COUNT IN THIS CASE.
048186,001644: 
048187,001645: 00,2176           07226                           TC       TPAGREE                               #  MAY CAUSE UPSHIFT OF ONE EXTRA PLACE.
048188,001646: 
048189,001647: 00,2177           30154                           CA       MPAC                                  #  BEGIN NORMALIZATION LOOP.
048190,001648: 00,2200           12207                           TCF      TSLCTEST                              
048191,001649: 
048192,001650: 00,2201           24135        TSLCLOOP           INCR     MPTEMP                                #  INCREMENT SHIFT COUNTER.
048193,001651: 00,2202           00006                           EXTEND                                         
048194,001652: 00,2203           30156                           DCA      MPAC       +1                         
048195,001653: 00,2204           20156                           DAS      MPAC       +1                         
048196,001654: 00,2205           60154                           AD       MPAC                                  
048197,001655: 00,2206           26154                           ADS      MPAC                                  
048198,001656: 00,2207           60000        TSLCTEST           DOUBLE                                         #  SEE IF (ANOTHER) SHIFT IS REQUIRED.
048199,001657: 00,2210           54000                           OVSK                                           
048200,001658: 00,2211           12201                           TCF      TSLCLOOP                              #  YES - INCREMENT COUNT AND SHIFT AGAIN.
048201,001659: 
048202,001660: 00,2212           40135        ENDTSLC            CS       MPTEMP                                
048203,001661: 00,2213           16572                           TCF      STORE1                                #  STORE SHIFT COUNT AND RETURN TO DANZIG.
048204,001662: 

Page 1125

048206,001664:                                                                                                  #           THE FOLLOWING ROUTINES PROCESSES THE GENERAL SHIFT INSTRUCTIONS SR, SRR, SL, AND SLR.
048207,001665:                                                                                                  #  THE GIVEN ADDRESS IS DECODED AS FOLLOWS:
048208,001666: 
048209,001667:                                                                                                  #           BITS 1-7    SHIFT COUNT (SUBADDRESS) LESS THAN 125 DECIMAL.
048210,001668:                                                                                                  #           BIT 8       PSEUDO SIGN BIT (DETECTS CHANGE IN SIGN IN INDEXED SHIFTS).
048211,001669:                                                                                                  #           BIT 9       0 FOR LEFT SHIFT, AND 1 FOR RIGHT SHIFT.
048212,001670:                                                                                                  #           BIT 10      1 FOR TERMINAL ROUND ON SCALAR SHIFTS, 0 OTHERWISE.
048213,001671:                                                                                                  #           BITS 11-13  0.
048214,001672:                                                                                                  #           BIT 14      1.
048215,001673:                                                                                                  #           BIT 15      0.
048216,001674: 
048217,001675:                                                                                                  #  THE ABOVE ENCODING IS DONE BY THE YUL SYSTEM.
048218,001676: 
048219,001677: 
048220,001678: 00,2214           70116        GENSHIFT           MASK     ADDRWD                                #  GET SHIFT COUNT, TESTING FOR ZERO.
048221,001679: 00,2215           10000                           CCS      A                                     #  (ARRIVES WITH C(A) = LOW7).
048222,001680: 00,2216           12224                           TCF      GENSHFT2                              #  IF NON-ZERO, PROCEED WITH DECREMENTED CT
048223,001681: 
048224,001682: 00,2217           34701                           CAF      BIT10                                 #  ZERO SHIFT COUNT. NO SHIFTS NEEDED BUT
048225,001683: 00,2220           70116                           MASK     ADDRWD                                #  WE MIGHT HAVE TO ROUND MPAC ON SLR AND
048226,001684: 00,2221           10000                           CCS      A                                     #  SRR (SCALAR ONLY).
048227,001685: 00,2222           07105                           TC       ROUNDSUB                              
048228,001686: 00,2223           16030                           TCF      DANZIG                                
048229,001687: 
048230,001688: 00,2224           54135        GENSHFT2           TS       MPTEMP                                #  DECREMENTED SHIFT COUNT TO MPTEMP.
048231,001689: 00,2225           34703                           CAF      BIT8                                  #  TEST MEANING OF LOW SEVEN BIT COUNT IN
048232,001690: 00,2226           00006                           EXTEND                                         #  MPTEMP NOW.
048233,001691: 00,2227           70116                           MP       ADDRWD                                
048234,001692: 00,2230           76214                           MASK     LOW2                                  #  JUMPS ON SHIFT DIRECTION (BIT8) AND
048235,001693: 00,2231           50000                           INDEX    A                                     
048236,001694: 00,2232           12233                           TCF      +1                                    #  ORIGINAL SHIFT DIRECTION (BIT 9).
048237,001695: 00,2233           12332                           TCF      RIGHT-                                #  NEGATIVE SHIFT COUNT FOR SL OR SLR.
048238,001696: 00,2234           12342                           TCF      LEFT                                  #  SL OR SLR.
048239,001697: 00,2235           12336                           TCF      LEFT-                                 #  NEGATIVE SHIFT COUNT WITH SR OR SRR.
048240,001698: 

Page 1126

048242,001700:                                                                                                  #           GENERAL SHIFT RIGHT.
048243,001701: 
048244,001702: 00,2236           10163        RIGHT              CCS      MODE                                  #  SEE IF VECTOR OR SCALAR.
048245,001703: 00,2237           12277                           TCF      GENSCR                                
048246,001704: 00,2240           12277                           TCF      GENSCR                                
048247,001705: 
048248,001706: 00,2241           30135                           CA       MPTEMP                                #  SEE IF SHIFT COUNT LESS THAN 14D.
048249,001707: 00,2242           63726        VRIGHT2            AD       NEG12                                 
048250,001708: 00,2243           00006                           EXTEND                                         
048251,001709: 00,2244           62127                           BZMF     VSSR                                  #  IF SO, BRANCH AND SHIFT IMMEDIATELY.
048252,001710: 
048253,001711: 00,2245           67716                           AD       NEGONE                                #  IF NOT, REDUCE MPTEMP BY A TOTAL OF 14,
048254,001712: 00,2246           54135                           TS       MPTEMP                                #  AND DO A SHIFT RIGHT AND ROUND BY 14.
048255,001713: 00,2247           34714                           CAF      ZERO                                  #  THE ROUND AT THIS STAGE MAY INTRODUCE A
048256,001714: 00,2250           54001                           TS       L                                     #  ONE BIT ERROR IN A SHIFT RIGHT 15D.
048257,001715: 00,2251           56154                           XCH      MPAC                                  
048258,001716: 00,2252           56155                           XCH      MPAC       +1                         
048259,001717: 00,2253           02272                           TC       SETROUND                              #  X COMPONENT NOW SHIFTED, SO MAKE UP THE
048260,001718: 00,2254           20155                           DAS      MPAC                                  #  ROUNDING QUANTITY (0 IN A AND 0 OR +-1
048261,001719:                                                                                                  #                                          IN L).
048262,001720: 00,2255           56157                           XCH      MPAC       +3                         #  REPEAT THE ABOVE PROCESS FOR Y AND Z.
048263,001721: 00,2256           56160                           XCH      MPAC       +4                         
048264,001722: 00,2257           02272                           TC       SETROUND                              
048265,001723: 00,2260           20160                           DAS      MPAC       +3                         #  NO OVERFLOW ON THESE ADDS.
048266,001724: 
048267,001725: 00,2261           56161                           XCH      MPAC       +5                         
048268,001726: 00,2262           56162                           XCH      MPAC       +6                         
048269,001727: 00,2263           02272                           TC       SETROUND                              
048270,001728: 00,2264           20162                           DAS      MPAC       +5                         
048271,001729: 
048272,001730: 00,2265           10135                           CCS      MPTEMP                                #  SEE IF DONE, DOING FINAL DECREMENT.
048273,001731: 00,2266           54135                           TS       MPTEMP                                
048274,001732: 00,2267           12242                           TCF      VRIGHT2                               
048275,001733: 00,2270           04604        BIASLO             DEC      .2974      B-1                        #  SQRT CONSTANT
048276,001734: 
048277,001735: 00,2271           16030                           TCF      DANZIG                                
048278,001736: 
048279,001737: 
048280,001738: 00,2272           60000        SETROUND           DOUBLE                                         #  MAKES UP ROUNDING QUANTITY FROM ARRIVING
048281,001739: 00,2273           54156                           TS       MPAC       +2                         #  C(A). L IS ZERO INITIALLY.
048282,001740: 00,2274           34714                           CAF      ZERO                                  
048283,001741: 00,2275           56001                           XCH      L                                     
048284,001742: 00,2276           00002                           TC       Q                                     #  RETURN AND DO THE DAS, RESETTING L TO 0.
048285,001743: 

Page 1127

048287,001745:                                                                                                  #           PROCESS SR AND SRR FOR SCALARS.
048288,001746: 
048289,001747: 00,2277           30135        GENSCR             CA       MPTEMP                                #  SEE IF THE ORIGINAL SHIFT COUNT WAS LESS
048290,001748: 00,2300           63726                 +1        AD       NEG12                                 #  THAN 14D.
048291,001749: 00,2301           00006                           EXTEND                                         
048292,001750: 00,2302           62322                           BZMF     DOSSHFT                               #  DO THE SHIFT IMMEDIATELY IF SO.
048293,001751: 
048294,001752: 00,2303           67716                 +4        AD       NEGONE                                #  IF NOT, DECREMENT SHIFT COUNT BY 14D AND
048295,001753: 00,2304           54135                           TS       MPTEMP                                #  SHIFT MPAC RIGHT 14 PLACES.
048296,001754: 00,2305           34714                           CAF      ZERO                                  
048297,001755: 00,2306           56154                           XCH      MPAC                                  
048298,001756: 00,2307           56155                           XCH      MPAC       +1                         
048299,001757: 00,2310           54156                           TS       MPAC       +2                         
048300,001758: 00,2311           10135                           CCS      MPTEMP                                #  SEE IF FINISHED, DO FINAL DECREMENT.
048301,001759: 00,2312           54135                           TS       MPTEMP                                
048302,001760: 00,2313           02300                           TC       GENSCR     +1                         
048303,001761: 00,2314           22650        SLOPEHI            DEC      .5884                                 #  SQRT CONSTANT.
048304,001762: 00,2315           34701                           CAF      BIT10                                 #  FINISHED WITH SHIFT. SEE IF ROUND
048305,001763: 00,2316           70116                           MASK     ADDRWD                                #  WANTED.
048306,001764: 00,2317           10000                           CCS      A                                     
048307,001765: 00,2320           07105                           TC       ROUNDSUB                              
048308,001766: 00,2321           16030                           TCF      DANZIG                                #  DO SO AND/OR EXIT.
048309,001767: 
048310,001768: 00,2322           50135        DOSSHFT            INDEX    MPTEMP                                #  PICK UP SHIFTING BIT.
048311,001769: 00,2323           34675                           CAF      BIT14                                 
048312,001770: 00,2324           54135                           TS       MPTEMP                                
048313,001771: 00,2325           34701                           CAF      BIT10                                 #  SEE IF TERMINAL ROUND DESIRED.
048314,001772: 00,2326           70116                           MASK     ADDRWD                                
048315,001773: 00,2327           10000                           CCS      A                                     
048316,001774: 00,2330           12031                           TCF      RIGHTR                                #  YES.
048317,001775: 00,2331           12033                           TCF      MPACSHR                               #  JUST SHIFT RIGHT.
048318,001776: 

Page 1128

048320,001778:                                                                                                  #           PROCESS THE RIGHT- (SL(R) WITH A NEGATIVE COUNT), LEFT-, AND LEFT OPTIONS.
048321,001779: 
048322,001780: 00,2332           40135        RIGHT-             CS       MPTEMP                                #  GET ABSOLUTE VALUE - 1 OF SHIFT COUNT
048323,001781: 00,2333           62126                           AD       OCT176                                #  UNDERSTANDING THAT BIT8 (PSEUDO-SIGN)
048324,001782: 00,2334           54135                           TS       MPTEMP                                #  WAS 1 INITIALLY.
048325,001783: 00,2335           12236                           TCF      RIGHT                                 #  DO NORMAL SHIFT RIGHT.
048326,001784: 
048327,001785: 00,2336           42126        LEFT-              CS       OCT176                                #  SAME PROLOGUE TO LEFT FOR INDEXED RIGHT
048328,001786: 00,2337           60135                           AD       MPTEMP                                #  SHIFTS WHOSE NET SHIFT COUNT IS NEGATIVE
048329,001787: 00,2340           40000                           COM                                            
048330,001788: 00,2341           54135                           TS       MPTEMP                                
048331,001789: 
048332,001790: 00,2342           10163        LEFT               CCS      MODE                                  #  SINCE LEFT SHIFTING IS SONE ONE PLACE AT
048333,001791: 00,2343           12346                           TCF      GENSCL                                #  A TIME, NO COMPARISON WITH 14 NEED BE
048334,001792: 00,2344           12346                           TCF      GENSCL                                #  DONE. FOR SCALARS, SEE IF TERMINAL ROUND
048335,001793: 00,2345           12145                           TCF      VSSL                                  #  DESIRED. FOR VECTORS, SHIFT IMMEDIATELY.
048336,001794: 
048337,001795: 00,2346           40116        GENSCL             CS       ADDRWD                                #  PUT ROUNDING BIT (BIT 10 OF ADDRWD)INTO
048338,001796: 00,2347           00006                           EXTEND                                         #  BIT 15 OF CYR WHERE THE ROUNDING BIT OF
048339,001797: 00,2350           74705                           MP       BIT6                                  #  A SHORT SHIFT LEFT WOULD BE
048340,001798: 00,2351           54020                           TS       CYR                                   
048341,001799: 00,2352           12103                           TCF      TSSL       +2                         #  DO THE SHIFT.
048342,001800: 

Page 1129

048344,001802:                                                                                                  #           SCALAR DIVISION INSTRUCTIONS, DDV AND BDDV, ARE EXECUTED HERE. AT THIS POINT, THE DIVIDEND IS IN MPAC
048345,001803:                                                                                                  #  AND THE DIVISOR IN BUF.
048346,001804: 
048347,001805: 00,2353           44712        DDV/BDDV           CS       ONE                                   #  INITIALIZATION.
048348,001806: 00,2354           54136                           TS       DVSIGN                                #  +-1 FOR POSITIVE QUOTIENT - -0 FOR NEG.
048349,001807: 00,2355           54137                           TS       DVNORMCT                              #  DIVIDEND NORMALIZATION COUNT.
048350,001808: 00,2356           54140                           TS       MAXDVSW                               #  NEAR-ONE DIVIDE FLAG.
048351,001809: 
048352,001810: 00,2357           10130                           CCS      BUF                                   #  FORCE BUF POSITIVE WITH THE MAJOR PART
048353,001811: 00,2360           12516                           TCF      BUFPOS                                #  NON-ZERO.
048354,001812: 00,2361           12363                           TCF      +2                                    
048355,001813: 00,2362           12531                           TCF      BUFNEG                                
048356,001814: 
048357,001815: 00,2363           54156        BUFZERO            TS       MPAC       +2                         #  ZERO THIS.
048358,001816: 00,2364           07226                           TC       TPAGREE                               #  FORCE SIGN AGREEMENT BEFORE OVERFLOW
048359,001817: 
048360,001818: 00,2365           10154                           CCS      MPAC                                  #  TEST TO SEE IF MPAC NON-ZERO.  (TOO BIG)
048361,001819: 00,2366           12414                           TCF      OVF+                                  #  MAJOR PART OF DIVIDEND IS POSITIVE NON-0
048362,001820: 00,2367           12371                           TCF      +2                                    
048363,001821: 00,2370           12413                           TCF      OVF+       -1                         #  MAJOR PART OF DIVIDEND IS NEG. NON-ZERO
048364,001822: 
048365,001823: 00,2371           56131                           XCH      BUF        +1                         #  SHIFT DIVIDEND AND DIVISOR LEFT 14.
048366,001824: 00,2372           56130                           XCH      BUF                                   
048367,001825: 00,2373           56155                           XCH      MPAC       +1                         
048368,001826: 00,2374           56154                           XCH      MPAC                                  
048369,001827: 00,2375           10130                           CCS      BUF                                   #  TRY AGAIN ON FORMER MINOR PART.
048370,001828: 00,2376           12422                           TCF      BUF+                                  
048371,001829: 00,2377           12401                           TCF      +2                                    #  OVERFLOW ON ZERO DIVISOR.
048372,001830: 00,2400           12416                           TCF      BUF-                                  
048373,001831: 
048374,001832: 00,2401           40154                           CS       MPAC                                  #  SIGN OF MPAC DETERMINES SIGN OF RESULT.
048375,001833: 00,2402           00006        SGNDVOVF           EXTEND                                         
048376,001834: 00,2403           62405                           BZMF     +2                                    
048377,001835: 00,2404           24136                           INCR     DVSIGN                                #  NEGMAX IN MPAC PERHAPS.
048378,001836: 00,2405           34672        DVOVF              CAF      POSMAX                                #  ON DIVISION OVERFLOW OF ANY SORT, SET
048379,001837: 00,2406           54154                           TS       MPAC                                  #  SET DP MPAC TO +-POSMAX.
048380,001838: 00,2407           02630                           TC       FINALDV    +3                         
048381,001839: 00,2410           34712                           CAF      ONE                                   #  SET OVERFLOW INDICATOR AND EXIT.
048382,001840: 00,2411           54121                           TS       OVFIND                                
048383,001841: 00,2412           06030                           TC       DANZIG                                
048384,001842: 
048385,001843: 
048386,001844: 00,2413           24136                 -1        INCR     DVSIGN                                
048387,001845: 00,2414           40131        OVF+               CS       BUF        +1                         #  LOAD LOWER ORDER PART OF DIVISOR.
048388,001846: 00,2415           12402                           TCF      SGNDVOVF                              #  GET SIGN OF RESULT.
048389,001847: 
048390,001848: 00,2416           00006        BUF-               EXTEND                                         #  IF BUF IS NEGATIVE, COMPLEMENT IT AND
048391,001849: 00,2417           40131                           DCS      BUF                                   #  MAINTAIN DVSIGN FOR FINAL QUOTIENT SIGN.
048392,001850: 00,2420           52131                           DXCH     BUF                                   
048393,001851: 00,2421           24136                           INCR     DVSIGN                                #  NOW -0.
048394,001852: 

Page 1130

048396,001854: 00,2422           10154        BUF+               CCS      MPAC                                  #  FORCE MPAC POSITIVE, CHECKING FOR ZERO
048397,001855: 00,2423           12437                           TCF      MPAC+                                 #  DIVIDEND IN THE PROCESS.
048398,001856: 00,2424           12426                           TCF      +2                                    
048399,001857: 00,2425           12433                           TCF      MPAC-                                 
048400,001858: 00,2426           10155                           CCS      MPAC       +1                         
048401,001859: 00,2427           12437                           TCF      MPAC+                                 
048402,001860: 00,2430           16030                           TCF      DANZIG                                #  EXIT IMMEDIATELY ON ZERO DIVIDEND.
048403,001861: 00,2431           12433                           TCF      MPAC-                                 
048404,001862: 00,2432           16030                           TCF      DANZIG                                
048405,001863: 
048406,001864: 00,2433           00006        MPAC-              EXTEND                                         #  FORCE MPAC POSITIVE AS BUF IN BUF-.
048407,001865: 00,2434           40155                           DCS      MPAC                                  
048408,001866: 00,2435           52155                           DXCH     MPAC                                  
048409,001867: 00,2436           24136                           INCR     DVSIGN                                #  NOW +1 OR -0.
048410,001868: 

Page 1131

048412,001870: 00,2437           40154        MPAC+              CS       MPAC                                  #  CHECK FOR DIVISION OVERFLOW. IF THE
048413,001871: 00,2440           67716                           AD       NEGONE                                #  MAJOR PART OF THE DIVIDEND IS LESS THAN
048414,001872: 00,2441           60130                           AD       BUF                                   #  THE MAJOR PART OF THE DIVISOR BY AT
048415,001873: 00,2442           10000                           CCS      A                                     #  LEAST TWO, WE CAN PROCEED IMMEDIATELY
048416,001874: 00,2443           12505                           TCF      DVNORM                                #  WITHOUT NORMALIZATION PRODUCING A DVMAX.
048417,001875: 00,2444           60001        -1/2+2             OCT      60001                                 #  USED IN SQRTSUB.
048418,001876: 
048419,001877: 00,2445           12446                           TCF      +1                                    #  IF THE ABOVE DOES NOT HOLD, FORCE SIGN
048420,001878: 00,2446           34675                           CAF      HALF                                  #  AGREEMENT IN NUMERATOR AND DENOMINATOR
048421,001879: 00,2447           60000                           DOUBLE                                         #  TO FACILITATE OVERFLOW AND NEAR-ONE
048422,001880: 00,2450           60155                           AD       MPAC       +1                         #  CHECKING.
048423,001881: 00,2451           54155                           TS       MPAC       +1                         
048424,001882: 00,2452           34714                           CAF      ZERO                                  
048425,001883: 00,2453           64672                           AD       POSMAX                                
048426,001884: 00,2454           26154                           ADS      MPAC                                  
048427,001885: 
048428,001886: 00,2455           34675                           CAF      HALF                                  #  SAME FOR BUF.
048429,001887: 00,2456           60000                           DOUBLE                                         
048430,001888: 00,2457           60131                           AD       BUF        +1                         
048431,001889: 00,2460           54131                           TS       BUF        +1                         
048432,001890: 00,2461           34714                           CAF      ZERO                                  
048433,001891: 00,2462           64672                           AD       POSMAX                                
048434,001892: 00,2463           26130                           ADS      BUF                                   
048435,001893: 
048436,001894: 00,2464           40154                           CS       MPAC                                  #  CHECK MAGNITUDE OF SIGN-CORRECTED
048437,001895: 00,2465           60130                           AD       BUF                                   #  OPERANDS.
048438,001896: 00,2466           10000                           CCS      A                                     
048439,001897: 00,2467           12505                           TCF      DVNORM                                #  DIVIDE OK - WILL NOT BECOME MAXDV CASE.
048440,001898: 00,2470           00133        LBUF2              ADRES    BUF2                                  
048441,001899: 00,2471           12405                           TCF      DVOVF                                 #  DIVISOR NOT LESS THAN DIVIDEND - OVF.
048442,001900: 
048443,001901: 00,2472           54140                           TS       MAXDVSW                               #  IF THE MAJOR PARTS OF THE DIVIDEND AND
048444,001902: 00,2473           40155                           CS       MPAC       +1                         #  DIVISOR ARE EQUAL, A SPECIAL APPROXIMA-
048445,001903: 00,2474           60131                           AD       BUF        +1                         #  TION IS USED (PROVIDED THE DIVISION IS
048446,001904: 00,2475           00006                           EXTEND                                         #  POSSIBLE, OF COURSE).
048447,001905: 00,2476           62405                           BZMF     DVOVF                                 
048448,001906: 00,2477           12505                           TCF      DVNORM                                #  IF NO OVERFLOW.
048449,001907: 

Page 1132

048451,001909: 00,2500           00006        BUFNORM            EXTEND                                         #  ADD -1 TO AUGMENT SHIFT COUNT AND SHIFT
048452,001910: 00,2501           24137                           AUG      DVNORMCT                              #  LEFT ONE PLACE.
048453,001911: 00,2502           00006                           EXTEND                                         
048454,001912: 00,2503           30131                           DCA      BUF                                   
048455,001913: 00,2504           20131                           DAS      BUF                                   
048456,001914: 
048457,001915: 00,2505           30130        DVNORM             CA       BUF                                   #  SEE IF DIVISOR NORMALIZED YET.
048458,001916: 00,2506           60000                           DOUBLE                                         
048459,001917: 00,2507           54000                           OVSK                                           
048460,001918: 00,2510           12500                           TCF      BUFNORM                               #  NO - SHIFT LEFT ONE AND TRY AGAIN.
048461,001919: 
048462,001920: 00,2511           52155                           DXCH     MPAC                                  #  CALL DIVIDEND NORMALIZATION SEQUENCE
048463,001921: 00,2512           50137                           INDEX    DVNORMCT                              #  PRIOR TO DOING THE DIVIDE.
048464,001922: 00,2513           02565                           TC       MAXTEST                               
048465,001923: 
048466,001924: 00,2514           54156                           TS       MPAC       +2                         #  RETURNS WITH DIVISION DONE AND C(A) = 0.
048467,001925: 00,2515           16030                           TCF      DANZIG                                
048468,001926: 
048469,001927: 00,2516           10000        BUFPOS             CCS      A                                     
048470,001928: 00,2517           12422                           TCF      BUF+                                  #  TO BUF+ IF BUF IS GREATER THAN +1.
048471,001929: 
048472,001930: 00,2520           40131                           CS       BUF        +1                         #  IF BUF IS +1, FORCING SIGN AGREEMENT
048473,001931: 00,2521           00006                           EXTEND                                         #  MAY CAUSE BUF TO BECOME ZERO.
048474,001932: 00,2522           62422                           BZMF     BUF+                                  #  BRANCH IF SIGNS AGREE.
048475,001933: 
048476,001934: 00,2523           34675                           CA       HALF                                  #  SIGNS DISAGREE.  FORCE AGREEMENT.
048477,001935: 00,2524           60000                 +6        DOUBLE                                         
048478,001936: 00,2525           26131                           ADS      BUF        +1                         
048479,001937: 00,2526           34714                           CA       ZERO                                  
048480,001938: 00,2527           54130                           TS       BUF                                   
048481,001939: 00,2530           12363                           TCF      BUFZERO                               
048482,001940: 
048483,001941: 
048484,001942: 00,2531           10000        BUFNEG             CCS      A                                     
048485,001943: 00,2532           12416                           TCF      BUF-                                  #  TO BUF- IF BUF IS LESS THAN -1.
048486,001944: 
048487,001945: 00,2533           30131                           CA       BUF        +1                         #  IF BUF IS -1, FORCING SIGN AGREEMENT
048488,001946: 00,2534           00006                           EXTEND                                         #  MAY CAUSE BUF TO BECOME ZERO.
048489,001947: 00,2535           62416                           BZMF     BUF-                                  #  BRANCH IF SIGNS AGREE.
048490,001948: 
048491,001949: 00,2536           44675                           CS       HALF                                  #  SIGNS DISAGREE.  FORCE AGREEMENT.
048492,001950: 00,2537           12524                           TCF      BUFPOS     +6                         
048493,001951: 

Page 1133

048495,001953:                                                                                                  #           THE FOLLOWING ARE PROLOGUES TO SHIFT THE DIVIDEND ARRIVING IN A AND L BEFORE THE DIVIDE.
048496,001954: 
048497,001955: 00,2540           22021                 -21D      LXCH     SR                                    #  SPECIAL PROLOGUE FOR UNIT WHEN THE
048498,001956: 00,2541           00006                           EXTEND                                         #  LENGTH OF THE ARGUMENT WAS NOT LESS THAN
048499,001957: 00,2542           74675                           MP       HALF                                  #  .5. IN THIS CASE, EACH COMPONENT MUST BE
048500,001958: 00,2543           56001                           XCH      L                                     #  SHIFTED RIGHT ONE TO PRODUCE A HALF-UNIT
048501,001959: 00,2544           60021                           AD       SR                                    #  VECTOR.
048502,001960: 00,2545           56001                           XCH      L                                     
048503,001961: 00,2546           12571                           TCF      GENDDV     +1                         #  WITH DP DIVIDEND IN A,L.
048504,001962: 
048505,001963: 00,2547           20001                           DDOUBL                                         #  PROLOGUE WHICH NORMALIZES THE DIVIDEND
048506,001964: 00,2550           20001                           DDOUBL                                         #  WHEN IT IS KNOWN THAT NO DIVISION
048507,001965: 00,2551           20001                           DDOUBL                                         #  OVERFLOW WILL OCCUR.
048508,001966: 00,2552           20001                           DDOUBL                                         
048509,001967: 00,2553           20001                           DDOUBL                                         
048510,001968: 00,2554           20001                           DDOUBL                                         
048511,001969: 00,2555           20001                           DDOUBL                                         
048512,001970: 00,2556           20001                           DDOUBL                                         
048513,001971: 00,2557           20001                           DDOUBL                                         
048514,001972: 00,2560           20001                           DDOUBL                                         
048515,001973: 00,2561           20001                           DDOUBL                                         
048516,001974: 00,2562           20001                           DDOUBL                                         
048517,001975: 00,2563           20001                           DDOUBL                                         
048518,001976: 00,2564           52155                           DXCH     MPAC                                  
048519,001977: 
048520,001978: 00,2565           10140        MAXTEST            CCS      MAXDVSW                               #  0 IF MAJORS MIGHT BE =, -1 OTHERWISE.
048521,001979: 00,2566           06552        BIASHI             DEC      .4192      B-1                        #  SQRT CONSTANTS
048522,001980: 
048523,001981: 00,2567           12642                           TCF      MAXDV                                 #  CHECK TO SEE IF THEY ARE NOW EQUAL.
048524,001982: 

Page 1134

048526,001984:                                                                                                  #           THE FOLLOWING IS A GENERAL PURPOSE DOUBLE PRECISION DIVISION ROUTINE. IT DIVIDES MPAC BY BUF AND LEAVES
048527,001985:                                                                                                  #  THE RESULT IN MPAC. THE FOLLOWING CONDITIONS MUST BE SATISFIED:
048528,001986: 
048529,001987:                                                                                                  #           1.  THE DIVISOR (BUF) MUST BE POSITIVE AND NOT LESS THAN .5.
048530,001988: 
048531,001989:                                                                                                  #           2.  THE DIVIDEND (MPAC) MUST BE POSITIVE WITH THE MAJOR PART OF MPAC STRICTLY LESS THAN THAT OF BUF
048532,001990:                                                                                                  #  (A SPECIAL APPROXIMATION, MAXDV, IS USED WHEN THE MAJOR PARTS ARE EQUAL).
048533,001991: 
048534,001992:                                                                                                  #           UNDERSTANDING THAT A/B = Q + S(R/B) WHERE S = 2(-14) AND Q AND R ARE QUOTIENT AND REMAINDER, RESPEC-
048535,001993:                                                                                                  #  TIVELY, THE FOLLOWING APPROXIMATION IS OBTAINED BY MULTIPLYING ABOVE AND BELOW BY C - SD AND NEGLECTING TERMS OF
048536,001994:                                                                                                  #  ORDER S-SQUARED (POSSIBLY INTRODUCING ERROR INTO THE LOW TWO BITS OF THE RESULT). SIGN AGREEMENT IS UNNECESSARY.
048537,001995: 
048538,001996:                                                                                                  #           A + SB .      (R - QD)                                             A + SB
048539,001997:                                                                                                  #           ------ = Q + S(------) WHERE Q AND R ARE QUOTIENT AND REMAINDER OF ------ RESPECTIVELY.
048540,001998:                                                                                                  #           C + SD        (  C   )                                                C
048541,001999: 
048542,002000: 00,2570           52155        GENDDV             DXCH     MPAC                                  #  WE NEED A AND B ONLY FOR FIRST DV.
048543,002001: 00,2571           00006                 +1        EXTEND                                         #  (SPECIAL UNIT PROLOGUE ENTERS HERE).
048544,002002: 00,2572           10130                           DV       BUF                                   #  A NOW CONTAINS Q AND L, R.
048545,002003: 00,2573           52155                           DXCH     MPAC                                  
048546,002004: 
048547,002005: 00,2574           40154                           CS       MPAC                                  #  FORM DIVIDEND FOR MINOR PART OF RESULT.
048548,002006: 00,2575           00006                           EXTEND                                         
048549,002007: 00,2576           70131                           MP       BUF        +1                         
048550,002008: 00,2577           60155                           AD       MPAC       +1                         #  OVERFLOW AT THIS POINT IS POSITIVE SINCE
048551,002009: 00,2600           54000                           OVSK                                           #  R IS POSITIVE IN EVERY CASE.
048552,002010: 00,2601           12606                           TCF      +5                                    
048553,002011: 
048554,002012: 00,2602           00006                           EXTEND                                         #  OVERFLOW CAN BE REMOVED BY SUBTRACTING C
048555,002013: 00,2603           60130                           SU       BUF                                   #  (BUF) ONCE SINCE R IS ALWAYS LESS THAN C
048556,002014: 00,2604           24154                           INCR     MPAC                                  #  IN THIS CASE. INCR COMPENSATES SUBTRACT.
048557,002015: 00,2605           12610                           TCF      +DOWN                                 #  (SINCE C(A) IS STILL POSITIVE).
048558,002016: 
048559,002017: 00,2606           00006                 +5        EXTEND                                         #  C(A) CAN BE MADE LESS THAN C IN MAGNI-
048560,002018: 00,2607           62620                           BZMF     -UP                                   #  TUDE BY DIMINISHING IT BY C (SINCE C IS
048561,002019:                                                                                                  #                                          NOT LESS THAN .5) UNLESS C(A) = 0.
048562,002020: 

Page 1135

048564,002022: 00,2610           00006        +DOWN              EXTEND                                         
048565,002023: 00,2611           60130                           SU       BUF                                   #  IF POSITIVE, REDUCE ONLY IF NECESSARY
048566,002024: 00,2612           00006                           EXTEND                                         #  SINCE THE COMPENSATING INCR MIGHT CAUSE
048567,002025: 00,2613           12616                           BZF      +3                                    #  OVERFLOW.
048568,002026: 00,2614           00006                           EXTEND                                         #  DONT SUBTRACT UNLESS RESULT IS POSITIVE
048569,002027: 00,2615           62624                           BZMF     ENDMAXDV                              #  OR ZERO.
048570,002028: 
048571,002029: 00,2616           24154                 +3        INCR     MPAC                                  #  KEEP SUBTRACT HERE AND COMPENSATE.
048572,002030: 00,2617           12625                           TCF      FINALDV                               
048573,002031: 
048574,002032: 00,2620           00006        -UP                EXTEND                                         #  IF ZERO, SET MINOR PART OF RESULT TO
048575,002033: 00,2621           12630                           BZF      FINALDV    +3                         #  ZERO.
048576,002034: 
048577,002035: 00,2622           00006                           EXTEND                                         #  IF NEGATIVE, ADD C TO A, SUBTRACTING ONE
048578,002036: 00,2623           26154                           DIM      MPAC                                  #  TO COMPENSATE. DIM IS OK HERE SINCE THE
048579,002037: 00,2624           60130        ENDMAXDV           AD       BUF                                   #  MAJOR PART NEVER GOES NEGATIVE.
048580,002038: 

Page 1136

048582,002040: 00,2625           22007        FINALDV            ZL                                             #  DO DV TO OBTAIN MINOR PART OF RESULT.
048583,002041: 00,2626           00006                           EXTEND                                         
048584,002042: 00,2627           10130                           DV       BUF                                   
048585,002043: 00,2630           54155                 +3        TS       MPAC       +1                         
048586,002044: 
048587,002045: 00,2631           10136                           CCS      DVSIGN                                #  LEAVE RESULT POSITIVE UNLESS C(DVSIGN)=
048588,002046: 00,2632           00002                           TC       Q                                     #  -0.
048589,002047: 00,2633           00002                           TC       Q                                     
048590,002048: 00,2634           00002                           TC       Q                                     
048591,002049: 
048592,002050: 00,2635           00006                           EXTEND                                         
048593,002051: 00,2636           40155                           DCS      MPAC                                  
048594,002052: 00,2637           52155                           DXCH     MPAC                                  
048595,002053: 00,2640           34714                           CAF      ZERO                                  #  SO WE ALWAYS RETURN WITH C(A) = 0.
048596,002054: 00,2641           00002                           TC       Q                                     
048597,002055: 

Page 1137

048599,002057:                                                                                                  #           IF THE MAJOR PARTS OF THE DIVISOR AND DIVIDEND ARE EQUAL, BUT THE MINOR PARTS ARE SUCH THAT THE
048600,002058:                                                                                                  #  DIVIDEND IS STRICTLY LESS THAN THE DIVISOR IN MAGNITUDE, THE FOLLOWING APPROXIMATION IS USED. THE ASSUMPTIONS
048601,002059:                                                                                                  #  ARE THE SAME AS THE GENERAL ROUTINE WITH THE ADDITION THAT SIGN AGREEMENT IS NECESSARY (B, C, & D POSITIVE).
048602,002060: 
048603,002061:                                                                                                  #                  C + SB .          (C + B - D)
048604,002062:                                                                                                  #                  ------ = 37777 + S(---------)
048605,002063:                                                                                                  #                  C + SD            (    C    )
048606,002064: 
048607,002065:                                                                                                  #           THE DIVISION MAY BE PERFORMED IMMEDIATELY SINCE B IS STRICTLY LESS THAN D AND C IS NOT LESS THAN .5.
048608,002066: 
048609,002067: 
048610,002068: 00,2642           40154        MAXDV              CS       MPAC                                  #  SEE IF MAXDV CASE STILL HOLDS AFTER
048611,002069: 00,2643           60130                           AD       BUF                                   #  NORMALIZATION.
048612,002070: 00,2644           00006                           EXTEND                                         
048613,002071: 00,2645           12647                           BZF      +2                                    
048614,002072: 00,2646           12570                           TCF      GENDDV                                #  MPAC NOW LESS THAN BUF - DIVIDE AS USUAL
048615,002073: 
048616,002074: 00,2647           34672                 +2        CAF      POSMAX                                #  SET MAJOR PART OF RESULT.
048617,002075: 00,2650           54154                           TS       MPAC                                  
048618,002076: 
048619,002077: 00,2651           40131                           CS       BUF        +1                         #  FORM DIVIDEND OF MINOR PART OF RESULT.
048620,002078: 00,2652           60155                           AD       MPAC       +1                         
048621,002079: 00,2653           12624                           TCF      ENDMAXDV                              #  GO ADD C AND DO DIVIDE, ATTACHING SIGN
048622,002080:                                                                                                  #                                          BEFORE EXITING.
048623,002081: 

Page 1138

048625,002083:                                                                                                  #           VECTOR DIVIDED BY SCALAR, V/SC, IS EXECUTED HERE. THE VECTOR IS NOW IN MPAC WITH SCALAR IN BUF.
048626,002084: 
048627,002085: 00,2654           44712        V/SC2              CS       ONE                                   #  INITIALIZE DIVIDEND NORMALIZATION COUNT
048628,002086: 00,2655           54137                           TS       DVNORMCT                              #  AND DIVISION SIGN REGISTER.
048629,002087: 00,2656           54127                           TS       VBUF       +5                         
048630,002088: 
048631,002089: 00,2657           03010                           TC       VECAGREE                              #  FORCE SIGN AGREEMENT IN VECTOR
048632,002090: 
048633,002091: 00,2660           52131                           DXCH     BUF                                   
048634,002092: 00,2661           07513                           TC       ALSIGNAG                              #  SIGN AGREE BUF
048635,002093: 00,2662           52131                           DXCH     BUF                                   
048636,002094: 00,2663           10130                           CCS      BUF                                   #  FORCE DIVISOR POSITIVE WITH MAJOR PART
048637,002095: 00,2664           12721                           TCF      /BUF+                                 #  NON-ZERO (IF POSSIBLE).
048638,002096: 00,2665           12667                           TCF      +2                                    
048639,002097: 00,2666           12715                           TCF      /BUF-                                 
048640,002098: 
048641,002099: 00,2667           56131                           XCH      BUF        +1                         #  SHIFT VECTOR AND SCALAR LEFT 14.
048642,002100: 00,2670           56130                           XCH      BUF                                   
048643,002101: 00,2671           56155                           XCH      MPAC       +1                         
048644,002102: 00,2672           56154                           XCH      MPAC                                  
048645,002103: 00,2673           00006                           EXTEND                                         #  CHECK FOR OVERFLOW IN EACH CASE.
048646,002104: 00,2674           12676                           BZF      +2                                    
048647,002105: 00,2675           12405                           TCF      DVOVF                                 
048648,002106: 
048649,002107: 00,2676           56160                           XCH      MPAC       +4                         
048650,002108: 00,2677           56157                           XCH      MPAC       +3                         
048651,002109: 00,2700           00006                           EXTEND                                         
048652,002110: 00,2701           12703                           BZF      +2                                    
048653,002111: 00,2702           12405                           TCF      DVOVF                                 
048654,002112: 
048655,002113: 00,2703           56162                           XCH      MPAC       +6                         
048656,002114: 00,2704           56161                           XCH      MPAC       +5                         
048657,002115: 00,2705           00006                           EXTEND                                         
048658,002116: 00,2706           12710                           BZF      +2                                    
048659,002117: 00,2707           12405                           TCF      DVOVF                                 
048660,002118: 
048661,002119: 00,2710           10130                           CCS      BUF                                   
048662,002120: 00,2711           12721                           TCF      /BUF+                                 
048663,002121: 00,2712           12405                           TCF      DVOVF                                 #  ZERO DIVISOR - OVERFLOW.
048664,002122: 00,2713           12715                           TCF      /BUF-                                 
048665,002123: 00,2714           12405                           TCF      DVOVF                                 
048666,002124: 
048667,002125: 00,2715           00006        /BUF-              EXTEND                                         #  ON NEGATIVE, COMPLEMENT BUF AND MAINTAIN
048668,002126: 00,2716           40131                           DCS      BUF                                   #  DVSIGN IN VBUF +5.
048669,002127: 00,2717           52131                           DXCH     BUF                                   
048670,002128: 00,2720           24127                           INCR     VBUF       +5                         
048671,002129: 

Page 1139

048673,002131: 00,2721           00006        /BUF+              EXTEND                                         
048674,002132: 00,2722           30131                           DCA      BUF                                   #  LEAVE ABS(ORIG DIVISOR) IN BUF2
048675,002133: 00,2723           52134                           DXCH     BUF2                                  #  FOR OVERFLOW TESTING
048676,002134: 00,2724           12732                           TCF      /NORM                                 #  NORMALIZE DIVISOR IN BUF.
048677,002135: 
048678,002136: 00,2725           00006        /NORM2             EXTEND                                         #  IF LESS THAN .5, AUGMENT DVNORMCT AND
048679,002137: 00,2726           24137                           AUG      DVNORMCT                              #  DOUBLE DIVISOR.
048680,002138: 00,2727           00006                           EXTEND                                         
048681,002139: 00,2730           30131                           DCA      BUF                                   
048682,002140: 00,2731           20131                           DAS      BUF                                   
048683,002141: 
048684,002142: 00,2732           30130        /NORM              CA       BUF                                   #  SEE IF DIVISOR NORMALIZED.
048685,002143: 00,2733           60000                           DOUBLE                                         
048686,002144: 00,2734           54000                           OVSK                                           
048687,002145: 00,2735           12725                           TCF      /NORM2                                #  DOUBLE AND TRY AGAIN IF NOT.
048688,002146: 
048689,002147: 00,2736           02750                           TC       V/SCDV                                #  DO X COMPONENT DIVIDE.
048690,002148: 00,2737           52160                           DXCH     MPAC       +3                         #  SUPPLY ARGUMENTS IN USUAL SEQUENCE.
048691,002149: 00,2740           52155                           DXCH     MPAC                                  
048692,002150: 00,2741           52160                           DXCH     MPAC       +3                         
048693,002151: 
048694,002152: 00,2742           02750                           TC       V/SCDV                                #  Y COMPONENT.
048695,002153: 00,2743           52162                           DXCH     MPAC       +5                         
048696,002154: 00,2744           52155                           DXCH     MPAC                                  
048697,002155: 00,2745           52162                           DXCH     MPAC       +5                         
048698,002156: 
048699,002157: 00,2746           02750                           TC       V/SCDV                                #  Z COMPONENT.
048700,002158: 00,2747           17367                           TCF      VROTATEX                              #  GO RE-ARRANGE COMPONENTS BEFORE EXIT.
048701,002159: 

Page 1140

048703,002161:                                                                                                  #           SUBROUTINE USED BY V/SC TO DIVIDE VECTOR COMPONENT IN MPAC,+1 BY THE SCALAR GIVEN IN BUF.
048704,002162: 
048705,002163: 00,2750           30127        V/SCDV             CA       VBUF       +5                         #  REFLECTS SIGN OF SCALAR.
048706,002164: 00,2751           54136                           TS       DVSIGN                                
048707,002165: 
048708,002166: 00,2752           10154                           CCS      MPAC                                  #  FORCE MPAC POSITIVE, EXITING ON ZERO.
048709,002167: 00,2753           12767                           TCF      /MPAC+                                
048710,002168: 00,2754           12756                           TCF      +2                                    
048711,002169: 00,2755           12763                           TCF      /MPAC-                                
048712,002170: 
048713,002171: 00,2756           10155                           CCS      MPAC       +1                         
048714,002172: 00,2757           12767                           TCF      /MPAC+                                
048715,002173: 00,2760           00002                           TC       Q                                     
048716,002174: 00,2761           12763                           TCF      /MPAC-                                
048717,002175: 00,2762           00002                           TC       Q                                     
048718,002176: 
048719,002177: 00,2763           00006        /MPAC-             EXTEND                                         #  USUAL COMPLEMENTING AND SETTING OF SIGN.
048720,002178: 00,2764           40155                           DCS      MPAC                                  
048721,002179: 00,2765           52155                           DXCH     MPAC                                  
048722,002180: 00,2766           24136                           INCR     DVSIGN                                
048723,002181: 
048724,002182: 00,2767           44712        /MPAC+             CS       ONE                                   #  INITIALIZE NEAR-ONE SWITCH.
048725,002183: 00,2770           54140                           TS       MAXDVSW                               
048726,002184: 
048727,002185: 00,2771           40154                           CS       MPAC                                  #  CHECK POSSIBLE OVERFLOW.
048728,002186: 00,2772           60133                           AD       BUF2                                  #  UNNORMALIZED INPUT DIVISOR.
048729,002187: 00,2773           10000                           CCS      A                                     
048730,002188: 00,2774           13004                           TCF      DDVCALL                               #  NOT NEAR-ONE
048731,002189: 00,2775           12777                           TCF      +2                                    #  +0 IS JUST POSSIBLE
048732,002190: 00,2776           12405                           TCF      DVOVF                                 #  NO HOPE
048733,002191: 00,2777           54140                           TS       MAXDVSW                               #  SIGNAL POSSIBLE NEAR-ONE CASE
048734,002192: 00,3000           40155                           CS       MPAC       +1                         #  SEE IF DIVISION CAN BE DONE
048735,002193: 00,3001           60134                           AD       BUF2       +1                         
048736,002194: 00,3002           00006                           EXTEND                                         
048737,002195: 00,3003           62405                           BZMF     DVOVF                                 
048738,002196: 
048739,002197: 00,3004           52155        DDVCALL            DXCH     MPAC                                  #  CALL PRE-DIVIDE NORMALIZATION.
048740,002198: 00,3005           50137                           INDEX    DVNORMCT                              
048741,002199: 00,3006           12565                           TCF      MAXTEST                               
048742,002200: 

Page 1141

048744,002202: 00,3007           32506        SLOPELO            DEC      .8324                                 
048745,002203: 
048746,002204: 00,3010           56002        VECAGREE           XCH      Q                                     #  SAVE Q IN A
048747,002205: 00,3011           52155                           DXCH     MPAC                                  
048748,002206: 00,3012           07513                           TC       ALSIGNAG                              #  SIGNAGREE MPAC
048749,002207: 00,3013           52155                           DXCH     MPAC                                  
048750,002208: 00,3014           52160                           DXCH     MPAC       +3                         
048751,002209: 00,3015           07513                           TC       ALSIGNAG                              #  SIGN AGREE MPAC +3
048752,002210: 00,3016           52160                           DXCH     MPAC       +3                         
048753,002211: 00,3017           52162                           DXCH     MPAC       +5                         
048754,002212: 00,3020           07513                           TC       ALSIGNAG                              #  SIGNAGREE MPAC +5
048755,002213: 00,3021           52162                           DXCH     MPAC       +5                         
048756,002214: 00,3022           00000                           TC       A                                     
048757,002215: 

Page 1142

048759,002217:                                                                                                  #           THE FOLLOWING ROUTINE EXECUTES THE UNIT INSTRUCTION, WHICH TAKES THE UNIT OF THE VECTOR IN MPAC.
048760,002218: 
048761,002219: 00,3023           03010        UNIT               TC       VECAGREE                              #  FORCE SIGN AGREEMENT IN VECTOR
048762,002220: 00,3024           07501                           TC       MPACVBUF                              #  SAVE ARGUMENT IN VBUF
048763,002221: 00,3025           34714                           CAF      ZERO                                  #  MUST SENSE OVERFLOW IN FOLLOWING DOT.
048764,002222: 00,3026           56121                           XCH      OVFIND                                
048765,002223: 00,3027           54141                           TS       TEM1                                  
048766,002224: 00,3030           03317                           TC       VSQSUB                                #  DOT MPAC WITH ITSELF.
048767,002225: 00,3031           30141                           CA       TEM1                                  
048768,002226: 00,3032           56121                           XCH      OVFIND                                
048769,002227: 00,3033           00006                           EXTEND                                         
048770,002228: 00,3034           13036                           BZF      +2                                    
048771,002229: 00,3035           12405                           TCF      DVOVF                                 
048772,002230: 00,3036           00006                           EXTEND                                         
048773,002231: 00,3037           30155                           DCA      MPAC                                  #  LEAVE THE SQUARE OF THE LENGTH OF THE
048774,002232: 00,3040           50120                           INDEX    FIXLOC                                #  ARGUMENT IN LVSQUARE.
048775,002233: 00,3041           52043                           DXCH     LVSQUARE                              
048776,002234: 
048777,002235: 00,3042           03343                           TC       SQRTSUB                               #  GO TAKE THE NORMALIZED SQUARE ROOT.
048778,002236: 
048779,002237: 00,3043           10154                           CCS      MPAC                                  #  CHECK FOR UNIT OVERFLOW.
048780,002238: 00,3044           13051                           TCF      +5                                    #  MPAC IS NOT LESS THAN .5 UNLESS
048781,002239: 00,3045           54001                           TS       L                                     
048782,002240: 00,3046           50120                           INDEX    FIXLOC                                
048783,002241: 00,3047           52045                           DXCH     LV                                    
048784,002242: 00,3050           12405                           TCF      DVOVF                                 #  INPUT TO SQRTSUB WAS 0.
048785,002243: 
048786,002244: 00,3051           44333                           CS       FOURTEEN                              #  SEE IF THE INPUT WAS SO SMALL THE THE
048787,002245: 00,3052           60135                           AD       MPTEMP                                #  FIRST TWO REGISTERS OF THE SQUARE WERE 0
048788,002246: 00,3053           10000                           CCS      A                                     
048789,002247: 00,3054           40000                           COM                                            #  IF SO, SAVE THE NEGATIVE OF THE SHIFT
048790,002248: 00,3055           13133                           TCF      SMALL                                 #  COUNT -15D.
048791,002249: 
048792,002250: 00,3056           13065                           TCF      LARGE                                 #  (THIS IS USUALLY THE CASE.)
048793,002251: 
048794,002252: 00,3057           44720                           CS       THIRTEEN                              #  IF THE SHIFT COUNT WAS EXACTLY 14, SET
048795,002253: 00,3060           54135                           TS       MPTEMP                                #  THE PRE-DIVIDE NORM COUNT TO -13D.
048796,002254: 
048797,002255: 00,3061           30154                           CA       MPAC                                  #  SHIFT THE LENGTH RIGHT 14 BEFORE STORING
048798,002256: 00,3062           54001        SMALL2             TS       L                                     #  (SMALL EXITS TO THIS POINT).
048799,002257: 00,3063           34714                           CAF      ZERO                                  
048800,002258: 00,3064           13112                           TCF      LARGE2                                #  GO TO STORE LENGTH AND PROCEED.
048801,002259: 
048802,002260: 00,3065           10135        LARGE              CCS      MPTEMP                                #  MOST ALL CASES COME HERE.
048803,002261: 00,3066           13074                           TCF      LARGE3                                #  SEE IF NO NORMALIZATION WAS REQUIRED BY
048804,002262: 
048805,002263: 00,3067           42024                           CS       SRDDV                                 #  SQRT, AND IF SO, SET UP FOR A SHIFT
048806,002264: 00,3070           54135                           TS       MPTEMP                                #  RIGHT 1 BEFORE DIVIDING TO PRODUCE
048807,002265: 00,3071           00006                           EXTEND                                         #  THE DESIRED HALF UNIT VECTOR.
048808,002266: 00,3072           30155                           DCA      MPAC                                  

Page 1143

048810,002268: 00,3073           13112                           TCF      LARGE2                                
048811,002269: 

Page 1144

048813,002271: 00,3074           40000        LARGE3             COM                                            #  LEAVE NEGATIVE OF SHIFT COUNT-1 FOR
048814,002272: 00,3075           54135                           TS       MPTEMP                                #  PREDIVIDE LEFT SHIFT.
048815,002273: 
048816,002274: 00,3076           40000                           COM                                            #  PICK UP REQUIRED SHIFTING BIT TO UNNORM-
048817,002275: 00,3077           50000                           INDEX    A                                     #  ALIZE THE SQRT RESULT.
048818,002276: 00,3100           34675                           CAF      BIT14                                 
048819,002277: 00,3101           54130                           TS       BUF                                   
048820,002278: 00,3102           00006                           EXTEND                                         
048821,002279: 00,3103           70155                           MP       MPAC       +1                         
048822,002280: 00,3104           56130                           XCH      BUF                                   
048823,002281: 00,3105           00006                           EXTEND                                         #  (UNNORMALIZE THE SQRT FOR LV).
048824,002282: 00,3106           70154                           MP       MPAC                                  
048825,002283: 00,3107           56001                           XCH      L                                     
048826,002284: 00,3110           60130                           AD       BUF                                   
048827,002285: 00,3111           56001                           XCH      L                                     
048828,002286: 
048829,002287: 00,3112           50120        LARGE2             INDEX    FIXLOC                                
048830,002288: 00,3113           52045                           DXCH     LV                                    #  LENGTH NOW STORED IN WORK AREA.
048831,002289: 
048832,002290: 00,3114           44712                           CS       ONE                                   
048833,002291: 00,3115           54140                           TS       MAXDVSW                               #  NO MAXDV CASES IN UNIT.
048834,002292: 
048835,002293: 00,3116           52123                           DXCH     VBUF                                  #  PREPARE X COMPONENT FOR DIVIDE, SETTING
048836,002294: 00,3117           52155                           DXCH     MPAC                                  #  LENGTH OF VECTOR AS DIVISOR IN BUF.
048837,002295: 00,3120           52131                           DXCH     BUF                                   
048838,002296: 00,3121           03151                           TC       UNITDV                                
048839,002297: 
048840,002298: 00,3122           52125                           DXCH     VBUF       +2                         #  DO Y AND Z IN USUAL FASHION SO WE CAN
048841,002299: 00,3123           52155                           DXCH     MPAC                                  #  EXIT THROUGH VROTATEX.
048842,002300: 00,3124           52160                           DXCH     MPAC       +3                         
048843,002301: 00,3125           03151                           TC       UNITDV                                
048844,002302: 
048845,002303: 00,3126           52127                           DXCH     VBUF       +4                         
048846,002304: 00,3127           52155                           DXCH     MPAC                                  
048847,002305: 00,3130           52162                           DXCH     MPAC       +5                         
048848,002306: 00,3131           03151                           TC       UNITDV                                
048849,002307: 00,3132           17367                           TCF      VROTATEX                              #  AND EXIT.
048850,002308: 

Page 1145

048852,002310:                                                                                                  #           IF THE LENGTH OF THE ARGUMENT VECTOR WAS LESS THAN 2(-28), EACH COMPONENT MUST BE SHIFTED LEFT AT LEAST
048853,002311:                                                                                                  #  14 PLACES BEFORE THE DIVIDE. NOTE THAT IN THIS CASE, THE MAJOR PART OF EACH COMPONENT IS ZERO.
048854,002312: 
048855,002313: 00,3133           54135        SMALL              TS       MPTEMP                                #  NEGATIVE OF PRE-DIVIDE SHIFT COUNT.
048856,002314: 
048857,002315: 00,3134           34714                           CAF      ZERO                                  #  SHIFT EACH COMPONENT LEFT 14.
048858,002316: 00,3135           56123                           XCH      VBUF       +1                         
048859,002317: 00,3136           56122                           XCH      VBUF                                  
048860,002318: 00,3137           56125                           XCH      VBUF       +3                         
048861,002319: 00,3140           56124                           XCH      VBUF       +2                         
048862,002320: 00,3141           56127                           XCH      VBUF       +5                         
048863,002321: 00,3142           56126                           XCH      VBUF       +4                         
048864,002322: 
048865,002323: 00,3143           40135                           CS       MPTEMP                                
048866,002324: 00,3144           50000                           INDEX    A                                     
048867,002325: 00,3145           34675                           CAF      BIT14                                 
048868,002326: 00,3146           00006                           EXTEND                                         
048869,002327: 00,3147           70154                           MP       MPAC                                  
048870,002328: 00,3150           13062                           TCF      SMALL2                                
048871,002329: 
048872,002330: 00,3151     4720               THIRTEEN           =        OCT15                                 
048873,002331: 00,3151     4333               FOURTEEN           =        OCT16                                 
048874,002332: 00,3151     4333               OCT16              =        R1D1                                  
048875,002333: 

Page 1146

048877,002335:                                                                                                  #           THE FOLLOWING ROUTINE SETS UP THE CALL TO THE DIVIDE ROUTINES.
048878,002336: 
048879,002337: 00,3151           10154        UNITDV             CCS      MPAC                                  #  FORCE MPAC POSITIVE IF POSSIBLE, SETTING
048880,002338: 00,3152           13170                           TCF      UMPAC+                                #  DVSIGN ACCORDING TO THE SIGN OF MPAC
048881,002339: 00,3153           13155                           TCF      +2                                    #  SINCE THE DIVISOR IS ALWAYS POSITIVE
048882,002340: 00,3154           13162                           TCF      UMPAC-                                #  HERE.
048883,002341: 
048884,002342: 00,3155           10155                           CCS      MPAC       +1                         
048885,002343: 00,3156           13170                           TCF      UMPAC+                                
048886,002344: 00,3157           00002                           TC       Q                                     #  EXIT IMMEDIATELY ON ZERO.
048887,002345: 00,3160           13162                           TCF      UMPAC-                                
048888,002346: 00,3161           00002                           TC       Q                                     
048889,002347: 
048890,002348: 00,3162           44714        UMPAC-             CS       ZERO                                  #  IF NEGATIVE, SET -0 IN DVSIGN FOR FINAL
048891,002349: 00,3163           54136                           TS       DVSIGN                                #  COMPLEMENT.
048892,002350: 00,3164           00006                           EXTEND                                         
048893,002351: 00,3165           40155                           DCS      MPAC                                  #  PICK UP ABSOLUTE VALUE OF ARG AND JUMP.
048894,002352: 00,3166           50135                           INDEX    MPTEMP                                
048895,002353: 00,3167           12564                           TCF      MAXTEST    -1                         
048896,002354: 
048897,002355: 00,3170           54136        UMPAC+             TS       DVSIGN                                #  SET DVSIGN FOR POSITIVE QUOTIENT.
048898,002356: 00,3171           52155                           DXCH     MPAC                                  
048899,002357: 00,3172           50135                           INDEX    MPTEMP                                
048900,002358: 00,3173           12564                           TCF      MAXTEST    -1                         
048901,002359: 

Page 1147

048903,002361:                                                                                                  #           MISCELLANEOUS UNARY OPERATIONS.
048904,002362: 
048905,002363: 00,3174           03300        DSQ                TC       DSQSUB                                #  SQUARE THE DP CONTENTS OF MPAC.
048906,002364: 00,3175           16030                           TCF      DANZIG                                
048907,002365: 
048908,002366: 00,3176           10163        ABVALABS           CCS      MODE                                  #  ABVAL OR ABS INSTRUCTION.
048909,002367: 00,3177           13226                           TCF      ABS                                   #  DO ABS ON SCALAR.
048910,002368: 00,3200           13226                           TCF      ABS                                   
048911,002369: 
048912,002370: 00,3201           03317        ABVAL              TC       VSQSUB                                #  DOT MPAC WITH ITSELF.
048913,002371: 00,3202           22163                           LXCH     MODE                                  #  MODE IS NOW DP (L ZERO AFTER DAS).
048914,002372: 
048915,002373: 00,3203           00006                           EXTEND                                         #  STORE SQUARE OF LENGTH IN WORK AREA.
048916,002374: 00,3204           30155                           DCA      MPAC                                  
048917,002375: 00,3205           50120                           INDEX    FIXLOC                                
048918,002376: 00,3206           52043                           DXCH     LVSQUARE                              
048919,002377: 

Page 1148

048921,002379:                                                                                                  #  PROGRAM DESCRIPTION- SUBROUTINE SQRT
048922,002380:                                                                                                  #  FUNCTIONAL DESCRIPTION-DOUBLE PRECISION SQUARE ROOT ROUTINE
048923,002381:                                                                                                  #      THIS PROGRAM TAKES THE SQUARE ROOT OF THE 27 OR 28 MOST SIGNIFICANT BITS IN THE TRIPLE PRECISION SET OF
048924,002382:                                                                                                  #      NUMBERS-MPAC,MPAC+1,AND MPAC+2.  THE ROOT IS RETURNED DOUBLE        PRECISION IN MPAC AND MPAC+1.
048925,002383:                                                                                                  #  WARNING- THIS SUBROUTINE USES A TRIPLE PRECISION INPUT. THE PROGRAMMER  MUST ASSURE THE CONTENTS OF MPAC+2
048926,002384:                                                                                                  #      ESPECIALLY IF THE CONTENTS OF MPAC IS SMALL OR ZERO.  FOR DETAILS SEE STG MEMO NO.949.
048927,002385:                                                                                                  #  CALLING SEQUENCE- IN INTERPRETIVE MODE I.E., FOLLOWING TC   INTPRET,SQRT  NO ADDRESS IS ALLOWED
048928,002386:                                                                                                  #  INPUT SCALING  THE BINARY POINT IS ASSUMED TO THE RIGHT OF BIT 15. THE  ANSWER IS RETURNED WITH THE SAME SCALING
048929,002387:                                                                                                  #  SUBROUTINES- GENSCR,MPACSHR, SQRTSUB,ABORT
048930,002388:                                                                                                  #  ABORT EXIT MODE- ABORTS ON NEGATIVE INPUT -1.2X10E-4 (77775  OCTAL)     OR LESS.
048931,002389:                                                                                                  #      DISPLAYS ERROR CODE 1302
048932,002390:                                                                                                  #                  TC   ABORT
048933,002391:                                                                                                  #                  OCT  1302
048934,002392:                                                                                                  #  DEBRIS -  LOCATIONS BUF,MPTEMP,ADDRWD ARE USED
048935,002393: 00,3207           03343        SQRT               TC       SQRTSUB                               #  TAKE THE SQUARE ROOT OF MPAC.
048936,002394: 00,3210           10135                           CCS      MPTEMP                                #  RETURNED NORMALIZED SQUARE ROOT. SEE IF
048937,002395: 00,3211           13213                           TCF      +2                                    #  ANY UN-NORMALIZATION REQUIRED AND EXIT
048938,002396: 00,3212           16030                           TCF      DANZIG                                #  IF NOT.
048939,002397: 
048940,002398: 00,3213           63726                           AD       NEG12                                 #  A RIGHT SHIFT OF MORE THAN 13 COULD BE
048941,002399: 00,3214           00006                           EXTEND                                         #  REQUIRED IF INPUT WAS ZERO IN MPAC,+1.
048942,002400: 00,3215           63221                           BZMF     SQRTSHFT                              #  GOES HERE IN MOST CASES.
048943,002401: 00,3216           22007                           ZL                                             #  IF A LONG SHIFT IS REQUIRED, GO TO
048944,002402: 00,3217           22116                           LXCH     ADDRWD                                #  GENERAL RIGHT SHIFT ROUTINES.
048945,002403: 00,3220           12303                           TCF      GENSCR     +4                         #  ADDRWD WAS ZERO TO PREVENT ROUND.
048946,002404: 
048947,002405: 00,3221           50135        SQRTSHFT           INDEX    MPTEMP                                #  SELECT SHIFTING BIT AND EXIT THROUGH
048948,002406: 00,3222           34674                           CAF      BIT15                                 #  SHIFT ROUTINES.
048949,002407: 00,3223           54135                           TS       MPTEMP                                
048950,002408: 00,3224           34714                           CAF      ZERO                                  #  TO ZERO MPAC +2 IN THE PROCESS.
048951,002409: 00,3225           12036                           TCF      MPACSHR    +3                         
048952,002410: 
048953,002411: 00,3226           06672        ABS                TC       BRANCH                                #  TEST SIGN OF MPAC AND COMPLEMENT IF
048954,002412: 00,3227           16030                           TCF      DANZIG                                
048955,002413: 00,3230           16030                           TCF      DANZIG                                
048956,002414: 00,3231           17637                           TCF      COMP                                  
048957,002415: 

Page 1149

048959,002417: 00,3232           44710        VDEF               CS       FOUR                                  #  VECTOR DEFINE - ESSENTIALLY TREATS
048960,002418: 00,3233           26166                           ADS      PUSHLOC                               #  SCALAR IN MPAC AS X COMPONENT, PUSHES UP
048961,002419: 00,3234           00006                           EXTEND                                         #  FOR Y AND THEN AGAIN FOR Z.
048962,002420: 00,3235           50000                           INDEX    A                                     
048963,002421: 00,3236           30003                           DCA      2                                     
048964,002422: 00,3237           52160                           DXCH     MPAC       +3                         
048965,002423: 00,3240           00006                           EXTEND                                         
048966,002424: 00,3241           50166                           INDEX    PUSHLOC                               
048967,002425: 00,3242           30001                           DCA      0                                     
048968,002426: 00,3243           52162                           DXCH     MPAC       +5                         
048969,002427: 00,3244           16470                           TCF      VMODE                                 #  MODE IS NON VECTOR.
048970,002428: 
048971,002429: 00,3245           03317        VSQ                TC       VSQSUB                                #  DOT MPAC WITH ITSELF.
048972,002430: 00,3246           17301                           TCF      DMODE                                 #  MODE IS NOW DP.
048973,002431: 
048974,002432: 00,3247           00006        PUSH               EXTEND                                         #  PUSH DOWN MPAC LEAVING IT LOADED.
048975,002433: 00,3250           30155                           DCA      MPAC                                  
048976,002434: 00,3251           50166                           INDEX    PUSHLOC                               #  PUSH DOWN FIRST TWO REGISTERS IN EACH
048977,002435: 00,3252           52001                           DXCH     0                                     
048978,002436: 
048979,002437: 00,3253           50163                           INDEX    MODE                                  #  INCREMENT PUSHDOWN POINTER.
048980,002438: 00,3254           36213                           CAF      NO.WDS                                
048981,002439: 00,3255           26166                           ADS      PUSHLOC                               
048982,002440: 
048983,002441: 00,3256           10163                           CCS      MODE                                  
048984,002442: 00,3257           13272                           TCF      TPUSH                                 #  PUSH DOWN MPAC +2.
048985,002443: 00,3260           16030                           TCF      DANZIG                                #  DONE FOR DP.
048986,002444: 
048987,002445: 00,3261           00006                           EXTEND                                         #  ON VECTOR, PUSH DOWN Y AND Z COMPONENTS.
048988,002446: 00,3262           30160                           DCA      MPAC       +3                         
048989,002447: 00,3263           50166                           INDEX    PUSHLOC                               
048990,002448: 00,3264           51775                           DXCH     0          -4                         
048991,002449: 00,3265           00006                           EXTEND                                         
048992,002450: 00,3266           30162                           DCA      MPAC       +5                         
048993,002451: 00,3267           50166                           INDEX    PUSHLOC                               
048994,002452: 00,3270           51777                           DXCH     0          -2                         
048995,002453: 00,3271           16030                           TCF      DANZIG                                
048996,002454: 
048997,002455: 00,3272           30156        TPUSH              CA       MPAC       +2                         
048998,002456: 00,3273           16523                           TCF      ENDTPUSH   +2                         
048999,002457: 
049000,002458: 00,3274           50120        RVQ                INDEX    FIXLOC                                #  RVQ - RETURN IVA QPRET.
049001,002459: 00,3275           30052                           CA       QPRET                                 
049002,002460: 00,3276           54117                           TS       POLISH                                
049003,002461: 00,3277           16621                           TCF      GOTO       +4                         #  (ASSUME QPRET POINTS TO FIXED ONLY.)
049004,002462: 

Page 1150

049006,002464:                                                                                                  #           THE FOLLOWING SUBROUTINES ARE USED IN SQUARING MPAC, IN BOTH THE SCALAR AND VECTOR SENSE. THEY ARE
049007,002465:                                                                                                  #  SPECIAL CASES OF DMPSUB AND DOTSUB, PUT IN TO SAVE SOME TIME.
049008,002466: 
049009,002467: 00,3300           30155        DSQSUB             CA       MPAC       +1                         #  SQUARES THE SCALAR CONTENTS OF MPAC.
049010,002468: 00,3301           00006                           EXTEND                                         
049011,002469: 00,3302           70000                           SQUARE                                         
049012,002470: 00,3303           54156                           TS       MPAC       +2                         
049013,002471: 00,3304           34714                           CAF      ZERO                                  #  FORM 2(CROSS TERM).
049014,002472: 00,3305           56155                           XCH      MPAC       +1                         
049015,002473: 00,3306           00006                           EXTEND                                         
049016,002474: 00,3307           70154                           MP       MPAC                                  
049017,002475: 00,3310           20001                           DDOUBL                                         #  AND MAYBE OVERFLOW.
049018,002476: 00,3311           20156                           DAS      MPAC       +1                         #  AND SET A TO NET OVERFLOW.
049019,002477: 00,3312           56154                           XCH      MPAC                                  
049020,002478: 00,3313           00006                           EXTEND                                         
049021,002479: 00,3314           70000                           SQUARE                                         
049022,002480: 00,3315           20155                           DAS      MPAC                                  
049023,002481: 00,3316           00002                           TC       Q                                     
049024,002482: 
049025,002483: 00,3317           00006        VSQSUB             EXTEND                                         #  DOTS THE VECTOR IN MPAC WITH ITSELF.
049026,002484: 00,3320           22137                           QXCH     DOTRET                                
049027,002485: 00,3321           03300                           TC       DSQSUB                                #  SQUARE THE X COMPONENT.
049028,002486: 00,3322           52160                           DXCH     MPAC       +3                         
049029,002487: 00,3323           52155                           DXCH     MPAC                                  
049030,002488: 00,3324           52131                           DXCH     BUF                                   #  SO WE CAN END IN DOTSUB.
049031,002489: 00,3325           30156                           CA       MPAC       +2                         
049032,002490: 00,3326           54132                           TS       BUF        +2                         
049033,002491: 
049034,002492: 00,3327           03300                           TC       DSQSUB                                #  SQUARE Y COMPONENT.
049035,002493: 00,3330           52156                           DXCH     MPAC       +1                         
049036,002494: 00,3331           20132                           DAS      BUF        +1                         
049037,002495: 00,3332           60154                           AD       MPAC                                  
049038,002496: 00,3333           60130                           AD       BUF                                   
049039,002497: 00,3334           54130                           TS       BUF                                   
049040,002498: 00,3335           13337                           TCF      +2                                    
049041,002499: 00,3336           54121                           TS       OVFIND                                #  IF OVERFLOW.
049042,002500: 
049043,002501: 00,3337           52162                           DXCH     MPAC       +5                         
049044,002502: 00,3340           52155                           DXCH     MPAC                                  
049045,002503: 00,3341           03300                           TC       DSQSUB                                #  SQUARE Z COMPONENT.
049046,002504: 00,3342           17154                           TCF      ENDDOT                                #  END AS IN DOTSUB.
049047,002505: 

Page 1151

049049,002507:                                                                                                  #           DOUBLE PRECISION SQUARE ROOT ROUTINE. TAKE THE SQUARE ROOT OF THE TRIPLE PRECISION (MPAC +2 USED ONLY
049050,002508:                                                                                                  #  IN NORMALIZATION) CONTENTS OF MPAC AND LEAVE THE NORMALIZED RESULT IN MPAC (C(MPAC) GREATER THAN OR EQUAL TO
049051,002509:                                                                                                  #  .5). THE RIGHT SHIFT COUNT (TO UNNORMALIZE) IS LEFT IN MPTEMP.
049052,002510: 
049053,002511: 
049054,002512: 00,3343           34714        SQRTSUB            CAF      ZERO                                  #  START BY ZEROING RIGHT SHIFT COUNT.
049055,002513: 00,3344           54135                           TS       MPTEMP                                
049056,002514: 
049057,002515: 00,3345           10154                           CCS      MPAC                                  #  CHECK FOR POSITIVE ARGUMENT, SHIFTING
049058,002516: 00,3346           13404                           TCF      SMPAC+                                #  FIRST SIGNIFICANT MPAC REGISTER INTO
049059,002517: 00,3347           13351                           TCF      +2                                    #  MPAC ITSELF.
049060,002518: 00,3350           13373                           TCF      SQRTNEG                               #  SEE IF MAG OF ARGUMENT LESS THAN 10(-4).
049061,002519: 
049062,002520: 00,3351           56156                           XCH      MPAC       +2                         #  MPAC IS ZERO - SHIFT LEFT 14.
049063,002521: 00,3352           56155                           XCH      MPAC       +1                         
049064,002522: 00,3353           54154                           TS       MPAC                                  
049065,002523: 00,3354           34716                           CAF      SEVEN                                 #  AUGMENT RIGHT SHIFT COUNTER.
049066,002524: 00,3355           54135                           TS       MPTEMP                                
049067,002525: 
049068,002526: 00,3356           10154                           CCS      MPAC                                  #  SEE IF MPAC NOW PNZ.
049069,002527: 00,3357           13404                           TCF      SMPAC+                                
049070,002528: 00,3360           13362                           TCF      +2                                    
049071,002529: 00,3361           13376                           TCF      ZEROANS                               #  NEGATIVE BUT LESS THAN 10(-4) IN MAG.
049072,002530: 
049073,002531: 00,3362           56155                           XCH      MPAC       +1                         #  ZERO - SHIFT LEFT 14 AGAIN.
049074,002532: 00,3363           54154                           TS       MPAC                                  
049075,002533: 00,3364           34716                           CAF      SEVEN                                 #  AUGMENT RIGHT SHIFT COUNTER.
049076,002534: 00,3365           26135                           ADS      MPTEMP                                
049077,002535: 
049078,002536: 00,3366           10154                           CCS      MPAC                                  
049079,002537: 00,3367           13404                           TCF      SMPAC+                                
049080,002538: 00,3370           00002                           TC       Q                                     #  SQRT(0) = 0.
049081,002539: 00,3371           13376                           TCF      ZEROANS                               
049082,002540: 00,3372           13452                           TCF      FIXROOT                               #  DO NOT LEAVE SQRTSUB WITH -0 IN MPAC.
049083,002541: 
049084,002542: 
049085,002543: 00,3373           10000        SQRTNEG            CCS      A                                     #  ARGUMENT IS NEGATIVE, BUT SEE IF SIGN-
049086,002544: 00,3374           13402                           TCF      SQRTABRT                              #  CORRECTED ARGUMENT IS LESS THAN 10(-4)
049087,002545: 
049088,002546: 00,3375           10155                           CCS      MPAC       +1                         #  IN MAGNITUDE. IF SO, CALL ANSWER ZERO.
049089,002547: 00,3376           34714        ZEROANS            CAF      ZERO                                  #  FORCE ANSWER TO ZERO HERE.
049090,002548: 00,3377           13452                           TCF      FIXROOT                               
049091,002549: 00,3400           13402                           TCF      SQRTABRT                              
049092,002550: 00,3401           13452                           TCF      FIXROOT                               
049093,002551: 
049094,002552: 00,3402           05622        SQRTABRT           TC       POODOO                                
049095,002553: 00,3403           01302                           OCT      1302                                  
049096,002554: 

Page 1152

049098,002556: 00,3404           62444        SMPAC+             AD       -1/2+2                                #  SEE IF ARGUMENT GREATER THAN OR EQUAL TO
049099,002557: 00,3405           00006                           EXTEND                                         #  .5.
049100,002558: 00,3406           63455                           BZMF     SRTEST                                #  IF SO, SEE IF LESS THAN .25.
049101,002559: 
049102,002560: 00,3407           52155                           DXCH     MPAC                                  #  WE WILL TAKE THE SQUARE ROOT OF MPAC/2.
049103,002561: 00,3410           22021                           LXCH     SR                                    #  SHIFT RIGHT 1 AND GO TO THE SQRT ROUTINE
049104,002562: 00,3411           00006                           EXTEND                                         
049105,002563: 00,3412           74675                           MP       HALF                                  
049106,002564: 00,3413           52155                           DXCH     MPAC                                  
049107,002565: 00,3414           56021                           XCH      SR                                    
049108,002566: 00,3415           26155                           ADS      MPAC       +1                         #  GUARANTEED NO OVERFLOW.
049109,002567: 
049110,002568: 00,3416           32314        ARGHI              CAF      SLOPEHI                               #  ARGUMENT BETWEEN .25 AND .5. GET A
049111,002569: 00,3417           00006                           EXTEND                                         #  LINEAR APPROXIMATION FOR THIS RANGE.
049112,002570: 00,3420           70154                           MP       MPAC                                  
049113,002571: 00,3421           62566                           AD       BIASHI                                #  X0/2 = (MPAC/2)(SLOPEHI) + BIASHI/2.
049114,002572: 
049115,002573: 00,3422           54130                 +4        TS       BUF                                   #  X0/2 (ARGLO ENTERS HERE).
049116,002574: 00,3423           30154                           CA       MPAC                                  #  SINGLE-PRECISION THROUGHOUT.
049117,002575: 00,3424           22007                           ZL                                             
049118,002576: 00,3425           00006                           EXTEND                                         
049119,002577: 00,3426           10130                           DV       BUF                                   #  (MPAC/2)/(X0/2)
049120,002578: 00,3427           00006                           EXTEND                                         
049121,002579: 00,3430           74675                           MP       HALF                                  
049122,002580: 00,3431           26130                           ADS      BUF                                   #  X1 = X0/2 + .5(MPAC/2)/(X0/2).
049123,002581: 
049124,002582: 00,3432           00006                           EXTEND                                         
049125,002583: 00,3433           74675                           MP       HALF                                  #  FORM UP X1/2.
049126,002584: 00,3434           52155                           DXCH     MPAC                                  #  SAVE AND BRING OUT ARGUMENT.
049127,002585: 00,3435           00006                           EXTEND                                         #  TAKE DP QUOTIENT WITH X1.
049128,002586: 00,3436           10130                           DV       BUF                                   
049129,002587: 00,3437           54131                           TS       BUF        +1                         #  SAVE MAJOR PART OF QUOTIENT.
049130,002588: 00,3440           34714                           CAF      ZERO                                  #  FORM MINOR PART OF QUOTIENT USING
049131,002589: 00,3441           56001                           XCH      L                                     #  (REMAINDER,0).
049132,002590: 00,3442           00006                           EXTEND                                         
049133,002591: 00,3443           10130                           DV       BUF                                   
049134,002592: 00,3444           54001                           TS       L                                     #  IN PREPARATION FOR DAS.
049135,002593: 00,3445           30131                           CA       BUF        +1                         
049136,002594: 00,3446           20155                           DAS      MPAC                                  #  X2 = X1/2 + (MPAC/2)X1
049137,002595: 
049138,002596: 00,3447           00006                           EXTEND                                         #  OVERFLOWS IF ARG. NEAR POSMAX.
049139,002597: 00,3450           13454                           BZF      TCQBNK00                              
049140,002598: 00,3451           34672                           CAF      POSMAX                                
049141,002599: 00,3452           54154        FIXROOT            TS       MPAC                                  
049142,002600: 00,3453           54155                           TS       MPAC       +1                         
049143,002601: 00,3454           00002        TCQBNK00           TC       Q                                     #  RETURN TO CALLER TO UNNORMALIZE, ETC.
049144,002602: 

Page 1153

049146,002604: 00,3455           64676        SRTEST             AD       QUARTER                               #  ARGUMENT WAS LESS THAN .5, SEE IF LESS
049147,002605: 00,3456           00006                           EXTEND                                         #  THAN .25.
049148,002606: 00,3457           63501                           BZMF     SQRTNORM                              #  IF SO, BEGIN NORMALIZATION.
049149,002607: 
049150,002608: 00,3460           52155                           DXCH     MPAC                                  #  IF BETWEEN .5 AND .25, SHIFT RIGHT 1 AND
049151,002609: 00,3461           22021                           LXCH     SR                                    #  START AT ARGLO.
049152,002610: 00,3462           00006                           EXTEND                                         
049153,002611: 00,3463           74675                           MP       HALF                                  
049154,002612: 00,3464           52155                           DXCH     MPAC                                  
049155,002613: 00,3465           56021                           XCH      SR                                    
049156,002614: 00,3466           26155                           ADS      MPAC       +1                         #  NO OVERFLOW.
049157,002615: 
049158,002616: 00,3467           33007        ARGLO              CAF      SLOPELO                               #  (NORMALIZED) ARGUMENT BETWEEN .125 AND
049159,002617: 00,3470           00006                           EXTEND                                         #  .25
049160,002618: 00,3471           70154                           MP       MPAC                                  
049161,002619: 00,3472           62270                           AD       BIASLO                                
049162,002620: 00,3473           13422                           TCF      ARGHI      +4                         #  BEGIN SQUARE ROOT.
049163,002621: 
049164,002622: 00,3474           00006        SQRTNM2            EXTEND                                         #  SHIFT LEFT 2 AND INCREMENT RIGHT SHIFT
049165,002623: 00,3475           30156                           DCA      MPAC       +1                         #  COUNT (FOR TERMINAL UNNORMALIZATION).
049166,002624: 00,3476           20156                           DAS      MPAC       +1                         
049167,002625: 00,3477           60154                           AD       MPAC                                  
049168,002626: 00,3500           26154                           ADS      MPAC                                  #  (NO OVERFLOW).
049169,002627: 
049170,002628: 00,3501           24135        SQRTNORM           INCR     MPTEMP                                #  FIRST TIME THROUGH, JUST SHIFT LEFT 1
049171,002629: 00,3502           00006                           EXTEND                                         #  (PUTS IN EFFECTIVE RIGHT SHIFT SINCE
049172,002630: 00,3503           30156                           DCA      MPAC       +1                         #  WE WANT MPAC/2).
049173,002631: 00,3504           20156                           DAS      MPAC       +1                         
049174,002632: 00,3505           60154                           AD       MPAC                                  
049175,002633: 00,3506           26154                           ADS      MPAC                                  #  (AGAIN NO OVERFLOW).
049176,002634: 00,3507           60000                           DOUBLE                                         
049177,002635: 00,3510           54022                           TS       CYL                                   
049178,002636: 
049179,002637: 00,3511           10022        NORMTEST           CCS      CYL                                   #  SEE IF ARGUMENT NOW NORMALIZED AT
049180,002638: 00,3512           10022                           CCS      CYL                                   #  GREATER THAN .125.
049181,002639: 00,3513           13474                           TCF      SQRTNM2                               #  NO - SHIFT LEFT 2 MORE AND TRY AGAIN.
049182,002640: 00,3514           13416                           TCF      ARGHI                                 #  YES - NOW BETWEEN .5 AND .25.
049183,002641: 00,3515           13467                           TCF      ARGLO                                 #  ARGUMENT NOW BETWEEN .25 AND .125.
049184,002642: 

Page 1154

049186,002644:                                                                                                  #  TRIGONOMETRIC FUNCTION PACKAGE.
049187,002645: 
049188,002646:                                                                                                  #           THE FOLLOWING TRIGONOMETRIC FUNCTIONS ARE AVAILABLE AS INTERPRETIVE OPERATIONS:
049189,002647: 
049190,002648:                                                                                                  #           1.  SIN                COMPUTES (1/2)SINE(2 PI MPAC).
049191,002649:                                                                                                  #           2.  COS                COMPUTES (1/2)COSINE(2 PI MPAC).
049192,002650: 
049193,002651:                                                                                                  #           3.  ASIN               COMPUTES (1/2PI)ARCSINE(2 MPAC).
049194,002652:                                                                                                  #           4.  ACOS               COMPUTES (1/2PI)ARCCOSINE(2 MPAC).
049195,002653: 
049196,002654:                                                                                                  #  SIN-ASIN AND COS-ACOS ARE MUTUALLY INVERSE, IE SIN(ASIN(X))  = X.
049197,002655: 
049198,002656: 
049199,002657: 00,3516           06672        COSINE             TC       BRANCH                                #  FINDS COSINE USING THE IDENTITY
049200,002658: 00,3517           13522                           TCF      +3                                    #  COS(X) = SIN(PI/2 - ABS(X)).
049201,002659: 00,3520           13525                           TCF      PRESINE                               
049202,002660: 00,3521           13525                           TCF      PRESINE                               
049203,002661: 
049204,002662: 00,3522           00006                 +3        EXTEND                                         
049205,002663: 00,3523           40155                           DCS      MPAC                                  
049206,002664: 00,3524           52155                           DXCH     MPAC                                  
049207,002665: 
049208,002666: 00,3525           34676        PRESINE            CAF      QUARTER                               #  PI/2 SCALED.
049209,002667: 00,3526           26154                           ADS      MPAC                                  
049210,002668: 
049211,002669: 
049212,002670: 00,3527           52155        SINE               DXCH     MPAC                                  #  DOUBLE ARGUMENT.
049213,002671: 00,3530           20001                           DDOUBL                                         
049214,002672: 00,3531           54000                           OVSK                                           #  SEE IF OVERFLOW PRESENT.
049215,002673: 00,3532           13535                           TCF      +3                                    #  IF NOT, ARGUMENT OK AS IS.
049216,002674: 
049217,002675: 00,3533           00006                           EXTEND                                         #  IF SO, WE LOST (OR GAINED) PI, SO
049218,002676: 00,3534           40001                           DCOM                                           #  COMPLEMENT MPAC USING THE IDENTITY
049219,002677:                                                                                                  #                                          SIN(X-(+)PI) = SIN(-X).
049220,002678: 00,3535           52155                 +3        DXCH     MPAC                                  
049221,002679: 00,3536           30154                           CA       MPAC                                  #  SEE IF ARGUMENT GREATER THAN .5 IN
049222,002680: 00,3537           60000                           DOUBLE                                         #  MAGNITUDE. IF SO, REDUCE IT TO LESS THAN
049223,002681: 00,3540           54001                           TS       L                                     #  .5 (+-PI/2 SCALED) AS FOLLOWS:
049224,002682: 00,3541           13552                           TCF      SN1                                   
049225,002683: 
049226,002684: 00,3542           50000                           INDEX    A                                     #  IF POSITIVE, FORM PI - X, IF NEGATIVE
049227,002685: 00,3543           34674                           CAF      NEG1/2     +1                         #  USE -PI - X.
049228,002686: 00,3544           60000                           DOUBLE                                         
049229,002687: 00,3545           00006                           EXTEND                                         
049230,002688: 00,3546           60154                           SU       MPAC                                  #  GUARANTEED NO OVERFLOW.
049231,002689: 00,3547           54154                           TS       MPAC                                  
049232,002690: 00,3550           40155                           CS       MPAC       +1                         
049233,002691: 00,3551           54155                           TS       MPAC       +1                         
049234,002692: 

Page 1155

049236,002694: 00,3552           00006        SN1                EXTEND                                         #  SET UP TO EVALUATE HASTINGS POLYNOMIAL
049237,002695: 00,3553           30155                           DCA      MPAC                                  
049238,002696: 00,3554           52134                           DXCH     BUF2                                  
049239,002697: 00,3555           03300                           TC       DSQSUB                                #  SQUARE MPAC.
049240,002698: 
049241,002699: 00,3556           07171                           TC       POLY                                  #  EVALUATE FOURTH ORDER POLYNOMIAL.
049242,002700: 00,3557           00003                           DEC      3          B-14                       
049243,002701: 00,3560           14441 37325                     2DEC     +.3926990796                            
049244,002702: 00,3562           53250 60764                     2DEC     -.6459637111                            
049245,002703: 00,3564           12146 21276                     2DEC     +.318758717                            
049246,002704: 00,3566           75466 71471                     2DEC     -.074780249                            
049247,002705: 00,3570           00236 32757                     2DEC     +.009694988                            
049248,002706: 
049249,002707: 00,3572           32470                           CAF      LBUF2                                 #  MULTIPLY BY ARGUMENT AND SHIFT LEFT 2.
049250,002708: 00,3573           07055                           TC       DMPSUB     -1                         
049251,002709: 
049252,002710: 00,3574           00006                           EXTEND                                         
049253,002711: 00,3575           30156                           DCA      MPAC       +1                         
049254,002712: 00,3576           20156                           DAS      MPAC       +1                         
049255,002713: 00,3577           60154                           AD       MPAC                                  
049256,002714: 00,3600           26154                           ADS      MPAC                                  #  NEITHER SHIFT OVERFLOWS.
049257,002715: 00,3601           00006                           EXTEND                                         
049258,002716: 00,3602           30156                           DCA      MPAC       +1                         
049259,002717: 00,3603           20156                           DAS      MPAC       +1                         
049260,002718: 00,3604           60154                           AD       MPAC                                  
049261,002719: 00,3605           26154                           ADS      MPAC                                  
049262,002720: 00,3606           16030                           TCF      DANZIG                                
049263,002721: 

Page 1156

049265,002723:                                                                                                  #           ARCSIN/ARCCOS ROUTINE.
049266,002724: 
049267,002725: 00,3607           33630        ARCSIN             CAF      LASINEX                               #  COMPUTE ARCSIN BY USING THE IDENTITY
049268,002726: 00,3610           13612                           TCF      +2                                    #  ARCSIN(X) = PI/2 - ARCCOS(X).
049269,002727: 
049270,002728: 00,3611           33712        ARCCOS             CAF      LDANZIG                               #  (EXITS IMMEDIATELY).
049271,002729: 00,3612           54136                           TS       ESCAPE                                
049272,002730: 00,3613           06672                           TC       BRANCH                                #  TEST SIGN OF INPUT.
049273,002731: 00,3614           13624                           TCF      ACOSST                                #  START IMMEDIATELY IF POSITIVE.
049274,002732: 00,3615           13724                           TCF      ACOSZERO                              #  ARCCOS(0) = PI/2 = .25.
049275,002733: 00,3616           00006                           EXTEND                                         #  IF NEGATIVE, USE THE IDENTITY
049276,002734: 00,3617           40155                           DCS      MPAC                                  #  ARCCOS(X) = PI - ARCCOS(-X), FORCING
049277,002735: 00,3620           52155                           DXCH     MPAC                                  #  ARGUMENT POSITIVE.
049278,002736: 00,3621           33727                           CAF      TCSUBTR                               #  SET EXIT  TO DO ABOVE BEFORE
049279,002737: 00,3622           56136                           XCH      ESCAPE                                #  ARCSIN/ARCCOS CONSIDERATIONS.
049280,002738: 00,3623           54137                           TS       ESCAPE2                               
049281,002739: 
049282,002740: 00,3624           44675        ACOSST             CS       HALF                                  #  TEST MAGNITUDE OF INPUT.
049283,002741: 00,3625           60154                           AD       MPAC                                  
049284,002742: 00,3626           10000                           CCS      A                                     
049285,002743: 00,3627           13720                           TCF      ACOSOVF                               #  THIS IS PROBABLY AN OVERFLOW CASE.
049286,002744: 
049287,002745: 00,3630           13706        LASINEX            TCF      ASINEX                                
049288,002746: 
049289,002747: 00,3631           13641                           TCF      ACOSST2                               #  NO OVERFLOW - PROCEED.
049290,002748: 
049291,002749: 00,3632           10155                           CCS      MPAC       +1                         #  IF MAJOR PART IS .5, CALL ANSWER 0
049292,002750: 00,3633           34714                           CAF      ZERO                                  #  UNLESS MINOR PART NEGATIVE.
049293,002751: 00,3634           13636                           TCF      ACOS=0                                
049294,002752: 
049295,002753: 00,3635           13641                           TCF      ACOSST2                               
049296,002754: 
049297,002755: 00,3636           54155        ACOS=0             TS       MPAC       +1                         
049298,002756: 00,3637           54154                           TS       MPAC                                  
049299,002757: 00,3640           00136                           TC       ESCAPE                                
049300,002758: 
049301,002759: 00,3641           00006        ACOSST2            EXTEND                                         #  NOW THAT ARGUMENT IS IN PROPER RANGE,
049302,002760: 00,3642           40155                           DCS      MPAC                                  #  BEGIN COMPUTATION. USE HASTINGS
049303,002761: 00,3643           64675                           AD       HALF                                  #  APPROXIMATION ARCCOS(X) = SQRT(1-X)P(X)
049304,002762: 00,3644           52155                           DXCH     MPAC                                  #  IN A SCALED VERSION WHERE P(X) IS A
049305,002763: 00,3645           52134                           DXCH     BUF2                                  #  SEVENTH ORDER POLYNOMIAL.
049306,002764: 
049307,002765: 00,3646           03343                           TC       SQRTSUB                               #  RETURNS WITH NORMALIZED SQUARE ROOT.
049308,002766: 
049309,002767: 00,3647           10135                           CCS      MPTEMP                                #  SEE IF UN-NORMALIZATION REQUIRED.
049310,002768: 00,3650           13713                           TCF      ACOSSHR                               #  IF SO.
049311,002769: 

Page 1157

049313,002771: 00,3651           52155        ACOS3              DXCH     MPAC                                  #  SET UP FOR POLYNOMIAL EVALUATION.
049314,002772: 00,3652           52134                           DXCH     BUF2                                  
049315,002773: 00,3653           52155                           DXCH     MPAC                                  
049316,002774: 
049317,002775: 00,3654           07171                           TC       POLY                                  
049318,002776: 00,3655           00006                           DEC      6          B-14                       
049319,002777: 00,3656           13240 23630                     2DEC     +.353553385                            #  COEFFICIENTS ARE C 2(+I)/PISQRT(2) WHERE
049320,002778: 00,3660           74721 47775                     2DEC*    -.0483017006 B+1*                       #               I
049321,002779: 00,3662           02440 20237                     2DEC*    +.0200273085 B+2*                       #  WHERE C STANDS FOR ORIGINAL COEFFS.
049322,002780: 00,3664           75067 70742                     2DEC*    -.0112931863 B+3*                       
049323,002781: 00,3666           03436 26756                     2DEC*    +.00695311612 B+4*                       
049324,002782: 00,3670           74037 57640                     2DEC*    -.00384617957 B+5*                       
049325,002783: 00,3672           03046 07143                     2DEC*    +.001501297736 B+6*                       
049326,002784: 00,3674           76654 42244                     2DEC*    -.000284160334 B+7*                       
049327,002785: 
049328,002786: 00,3676           32470                           CAF      LBUF2                                 #  DO FINAL MULTIPLY AND GO TO ANY
049329,002787: 00,3677           07055                           TC       DMPSUB     -1                         #  EPILOGUE SEQUENCES.
049330,002788: 00,3700           00136                           TC       ESCAPE                                
049331,002789: 
049332,002790: 00,3701           00006        SUBTR              EXTEND                                         #  EPILOGUE FOR NEGATIVE INPUTS TO ARCCOS.
049333,002791: 00,3702           40155                           DCS      MPAC                                  
049334,002792: 00,3703           64675                           AD       HALF                                  #  FORMS PI - ARCCOS(-X) = ARCCOS(X).
049335,002793: 00,3704           52155                           DXCH     MPAC                                  
049336,002794: 00,3705           00137                           TC       ESCAPE2                               #  GO TO POSSIBLE ARCSIN EPILOGUE.
049337,002795: 
049338,002796: 00,3706           00006        ASINEX             EXTEND                                         
049339,002797: 00,3707           40155                           DCS      MPAC                                  #  ARCSIN EPILOGUE - GET ARCSIN(X)
049340,002798: 00,3710           64676                           AD       QUARTER                               #  = PI/2 - ARCCOS(X).
049341,002799: 00,3711           52155                           DXCH     MPAC                                  
049342,002800: 00,3712           16030        LDANZIG            TCF      DANZIG                                
049343,002801: 

Page 1158

049345,002803: 00,3713           50000        ACOSSHR            INDEX    A                                     #  THE SHIFT RIGHT IS LESS THAN 14 SINCE
049346,002804: 00,3714           34675                           CAF      BIT14                                 #  THE INPUT WAS NON-ZERO DP.
049347,002805: 00,3715           54135                           TS       MPTEMP                                
049348,002806: 00,3716           02073                           TC       VSHRRND                               #  DP SHIFT RIGHT AND ROUND.
049349,002807: 00,3717           13651                           TCF      ACOS3                                 #  PROCEED.
049350,002808: 
049351,002809: 00,3720           00006        ACOSOVF            EXTEND                                         #  IF MAJOR PART WAS ONLY 1 MORE THAN .5,
049352,002810: 00,3721           13636                           BZF      ACOS=0                                #  CALL ANSWER ZERO.
049353,002811: 
049354,002812: 00,3722           05622        ACOSABRT           TC       POODOO                                
049355,002813: 00,3723           01301                           OCT      1301                                  
049356,002814: 
049357,002815: 00,3724           34676        ACOSZERO           CAF      QUARTER                               #  ACOS(0) = PI/2.
049358,002816: 00,3725           13637                           TCF      ACOS=0     +1                         #  SET MPAC AND EXIT VIA ESCAPE.
049359,002817: 
049360,002818: 00,3726           77763        NEG12              DEC      -12        B-14                       
049361,002819: 00,3727           13701        TCSUBTR            TCF      SUBTR                                 
049362,002820: 

Page 1159

049364,002822:                                                                                                  #           THE FOLLOWING INSTRUCTIONS ARE AVAILABLE FOR SETTING, MODIFYING, AND BRANCHING ON INDEX REGISTERS:
049365,002823: 
049366,002824:                                                                                                  #           1.  AXT                ADDRESS TO INDEX TRUE.
049367,002825:                                                                                                  #           1.  AXC                ADDRESS TO INDEX COMPLEMENTED.
049368,002826:                                                                                                  #           3.  LXA                LOAD INDEX FROM ERASABLE.
049369,002827:                                                                                                  #           4.  LXC                LOAD INDEX COMPLEMENTED FROM ERASABLE.
049370,002828:                                                                                                  #           5.  SXA                STORE INDEX IN ERASABLE.
049371,002829:                                                                                                  #           6.  XCHX               EXCHANGE INDEX REIGSTER WITH ERASABLE.
049372,002830: 
049373,002831:                                                                                                  #           7.  INCR               INCREMENT INDEX REGISTER.
049374,002832:                                                                                                  #           8.  XAD                ERASABLE ADD TO INDEX REGISTER.
049375,002833:                                                                                                  #           9.  XSU                ERASABLE SUBTRACT FROM INDEX REGISTER.
049376,002834: 
049377,002835:                                                                                                  #          10.  TIX                BRANCH ON INDEX REGISTER AND DECREMENT.
049378,002836: 
049379,002837: 
049380,002838: 01,2371                                           BANK     01                                    
049381,002839: 
049382,002840: 01,2371                                           COUNT    01/INTER                              
049383,002841: 
049384,002842: 01,2371           02466        AXT                TC       TAGSUB                                #  SELECT APPROPRIATE INDEX REGISTER.
049385,002843: 01,2372           30117                           CA       POLISH                                
049386,002844: 01,2373           50130        XSTORE             INDEX    INDEXLOC                              #  CONTAINS C(FIXLOC) OR C(FIXLOC)+1.
049387,002845: 01,2374           54046                           TS       X1                                    
049388,002846: 01,2375           16030                           TCF      DANZIG                                
049389,002847: 
049390,002848: 01,2376           02466        AXC                TC       TAGSUB                                
049391,002849: 01,2377           40117                           CS       POLISH                                
049392,002850: 01,2400           02373                           TC       XSTORE                                
049393,002851: 
049394,002852: 01,2401           02454        LXA                TC       15ADRERS                              #  LOAD INDEX REGISTER FROM ERASABLE.
049395,002853: 01,2402           50117                           INDEX    POLISH                                
049396,002854: 01,2403           30000                           CA       0                                     
049397,002855: 01,2404           12373                           TCF      XSTORE                                
049398,002856: 
049399,002857: 01,2405           02454        LXC                TC       15ADRERS                              #  LOAD NDX REG FROM ERASABLE COMPLEMENTED.
049400,002858: 01,2406           50117                           INDEX    POLISH                                
049401,002859: 01,2407           40000                           CS       0                                     
049402,002860: 01,2410           12373                           TCF      XSTORE                                
049403,002861: 
049404,002862: 01,2411           02454        SXA                TC       15ADRERS                              #  STORE INDEX REGISTER IN ERASABLE.
049405,002863: 01,2412           50130                           INDEX    INDEXLOC                              
049406,002864: 01,2413           30046                           CA       X1                                    
049407,002865: 01,2414           50117        MSTORE1            INDEX    POLISH                                
049408,002866: 01,2415           54000                           TS       0                                     
049409,002867: 01,2416           16030                           TCF      DANZIG                                
049410,002868: 

Page 1160

049412,002870: 01,2417           02454        XCHX               TC       15ADRERS                              #  EXCHANGE INDEX REGISTER WITH ERASABLE.
049413,002871: 01,2420           50117                           INDEX    POLISH                                
049414,002872: 01,2421           30000                           CA       0                                     
049415,002873: 01,2422           50130                           INDEX    INDEXLOC                              
049416,002874: 01,2423           56046                           XCH      X1                                    
049417,002875: 01,2424           12414                           TCF      MSTORE1                               
049418,002876: 
049419,002877: 01,2425           02454        XAD                TC       15ADRERS                              #  ADD ERASABLE TO INDEX REGISTER.
049420,002878: 01,2426           50117                           INDEX    POLISH                                
049421,002879: 01,2427           30000                           CA       0                                     
049422,002880: 01,2430           50130        XAD2               INDEX    INDEXLOC                              
049423,002881: 01,2431           26046                           ADS      X1                                    #  IGNORING OVERFLOWS.
049424,002882: 01,2432           16030                           TCF      DANZIG                                
049425,002883: 
049426,002884: 01,2433           02466        INCR               TC       TAGSUB                                #  INCREMENT INDEX REGISTER.
049427,002885: 01,2434           30117                           CA       POLISH                                
049428,002886: 01,2435           12430                           TCF      XAD2                                  
049429,002887: 
049430,002888: 01,2436           02454        XSU                TC       15ADRERS                              #  SUBTRACT ERASABLE FROM INDEX REGISTER.
049431,002889: 01,2437           50117                           INDEX    POLISH                                
049432,002890: 01,2440           40000                           CS       0                                     
049433,002891: 01,2441           12430                           TCF      XAD2                                  
049434,002892: 
049435,002893: 
049436,002894: 01,2442           02466        TIX                TC       TAGSUB                                #  BRANCH AND DECREMENT ON INDEX.
049437,002895: 01,2443           50130                           INDEX    INDEXLOC                              
049438,002896: 01,2444           40050                           CS       S1                                    
049439,002897: 01,2445           50130                           INDEX    INDEXLOC                              
049440,002898: 01,2446           60046                           AD       X1                                    
049441,002899: 01,2447           00006                           EXTEND                                         #  NO OPERATION IF DECREMENTED INDEX IS
049442,002900: 01,2450           66030                           BZMF     DANZIG                                #  NEGATIVE OR ZERO.
049443,002901: 
049444,002902: 01,2451           50130        DOTIXBR            INDEX    INDEXLOC                              
049445,002903: 01,2452           56046                           XCH      X1                                    #  IGNORING OVERFLOWS.
049446,002904: 
049447,002905: 01,2453           16615                           TCF      GOTO                                  #  DO THE BRANCH USING THE CADR IN POLISH.
049448,002906: 

Page 1161

049450,002908:                                                                                                  #           SUBROUTINE TO CONVERT AN ERASABLE ADDRESS (11 BITS) TO AN EBANK SETTING AND SUBADDRESS.
049451,002909: 
049452,002910: 01,2454           40117        15ADRERS           CS       POLISH                                
049453,002911: 01,2455           64727                           AD       DEC45                                 
049454,002912: 01,2456           10000                           CCS      A                                     #  DOES THE ADDRESS POINT TO THE WORK AREA?
049455,002913: 01,2457           30120                           CA       FIXLOC                                #  YES.  ADD FIXLOC.  EBANK OK AS IS.
049456,002914: 01,2460           12465                           TCF      +5                                    
049457,002915: 
049458,002916: 01,2461           34744                           CA       OCT1400                               #  NO.  SET EBANK & MAKE UP SUBADDRESS.
049459,002917: 01,2462           56117                           XCH      POLISH                                
049460,002918: 01,2463           54003                           TS       EBANK                                 
049461,002919: 01,2464           74373                           MASK     LOW8                                  
049462,002920: 01,2465           26117                 +5        ADS      POLISH                                #  FALL INTO TAGSUB, AND RETURN VIA Q.
049463,002921: 
049464,002922:                                                                                                  #           SUBROUTINE WHICH SETS THE ADDRESS OF THE SPECIFIED INDEX IN INDEXLOC. (ACTUALLY, THE ADDRESS -38D.)
049465,002923: 
049466,002924: 01,2466           30120        TAGSUB             CA       FIXLOC                                
049467,002925: 01,2467           54130                           TS       INDEXLOC                              
049468,002926: 
049469,002927: 01,2470           10020                           CCS      CYR                                   #  BIT 15 SPECIFIES INDEX.
049470,002928: 01,2471           24130                           INCR     INDEXLOC                              #  0 MEANS USE X2.
049471,002929: 01,2472           00002                           TC       Q                                     
049472,002930: 01,2473           00002                           TC       Q                                     #  1 FOR X1.
049473,002931: 

Page 1162

049475,002933:                                                                                                  #           MISCELLANEOUS OPERATION CODES WITH DIRECT ADDRESSES. INCLUDED HERE ARE:
049476,002934: 
049477,002935:                                                                                                  #           1.  ITA                STORE QPRET (RETURN ADDRESS) IN ERASABLE.
049478,002936:                                                                                                  #           2.  CALL               CALL A SUBROUTINE, LEAVING RETURN IN QPRET.
049479,002937:                                                                                                  #           3.  RTB                RETURN TO BASIC LANGUAGE AT THE GIVEN ADDRESS.
049480,002938:                                                                                                  #           4.  BHIZ               BRANCH IF THE HIGH ORDER OF MPAC IS ZERO (SINGLE PRECISION).
049481,002939:                                                                                                  #           5.  BOV                BRANCH ON OVERFLOW.
049482,002940:                                                                                                  #           6.  GOTO               SIMPLE SEQUENCE CHANGE.
049483,002941: 
049484,002942: 01,2474           10020        RTB/BHIZ           CCS      CYR                                   
049485,002943: 01,2475           30117        RTB                CA       POLISH                                
049486,002944: 01,2476           04560                           TC       SWCALL     -1                         #  SO A "TC Q" FROM ROUTINE LEADS TO DANZIG
049487,002945: 
049488,002946: 01,2477           10154        BHIZ               CCS      MPAC                                  
049489,002947: 01,2500           16030                           TCF      DANZIG                                
049490,002948: 01,2501           16615                           TCF      GOTO                                  
049491,002949: 01,2502           16030                           TCF      DANZIG                                
049492,002950: 01,2503           16615                           TCF      GOTO                                  
049493,002951: 
049494,002952: 01,2504           10121        BOV(B)             CCS      OVFIND                                #  BRANCH ON OVERFLOW TO BASIC OR INTERP.
049495,002953: 01,2505           12507                           TCF      +2                                    
049496,002954: 01,2506           16030                           TCF      DANZIG                                
049497,002955: 01,2507           54121                           TS       OVFIND                                
049498,002956: 01,2510           10020                           CCS      CYR                                   
049499,002957: 01,2511           12475                           TCF      RTB                                   #  IF BASIC.
049500,002958: 01,2512           00360        B5TOB8             OCT      360                                   
049501,002959: 01,2513           16615                           TCF      GOTO                                  
049502,002960: 

Page 1163

049504,002962: 01,2514           10020        BZE/GOTO           CCS      CYR                                   #  SEE WHICH OP-CODE IS DESIRED.
049505,002963: 01,2515           06672                           TC       BRANCH                                #  DO BZE.
049506,002964: 01,2516           16030                           TCF      DANZIG                                
049507,002965: 01,2517           16615                           TCF      GOTO                                  #  DO GOTO.
049508,002966: 01,2520           16030                           TCF      DANZIG                                
049509,002967: 
049510,002968: 01,2521           10020        BPL/BMN            CCS      CYR                                   
049511,002969: 01,2522           12530                           TCF      BPL                                   
049512,002970: 01,2523           12000        5B10               DEC      5          B+10                       #  SHIFTS OP CODE IN SWITCH INSTRUCTION ADR
049513,002971: 
049514,002972: 01,2524           06672                           TC       BRANCH                                #  DO BMN.
049515,002973: 01,2525           16030                           TCF      DANZIG                                
049516,002974: 01,2526           16030                           TCF      DANZIG                                
049517,002975: 01,2527           16615                           TCF      GOTO                                  #  ONLY IF NNZ.
049518,002976: 
049519,002977: 01,2530           06672        BPL                TC       BRANCH                                
049520,002978: 01,2531           16615                           TCF      GOTO                                  #  IF POSITIVE OR ZERO.
049521,002979: 01,2532           16615                           TCF      GOTO                                  
049522,002980: 01,2533           16030                           TCF      DANZIG                                
049523,002981: 
049524,002982: 01,2534           10020        CALL/ITA           CCS      CYR                                   
049525,002983: 01,2535           16607                           TCF      CALL                                  
049526,002984: 
049527,002985: 01,2536           05642                           TC       CCSHOLE                               
049528,002986: 01,2537           02454                           TC       15ADRERS                              #  STORE QPRET. (TAGSUB AFTER 15ADRERS IS
049529,002987: 01,2540           50120                           INDEX    FIXLOC                                #  SLOW IN THIS CASE, BUT SAVES STORAGE.)
049530,002988: 01,2541           30052                           CA       QPRET                                 
049531,002989: 01,2542           12414                           TCF      MSTORE1                               
049532,002990: 

Page 1164

049534,002992:                                                                                                  #           THE FOLLOWING OPERATIONS ARE AVAILABLE FOR ALTERING AND TESTING INTERPRETIVE SWITCHES:
049535,002993: 
049536,002994:                                                                                                  #  00       BONSET                 SET A SWITCH AND DO A GOTO IF IT WAS ON.
049537,002995:                                                                                                  #  01       SETGO                  SET A SWITCH AND DO A GOTO.
049538,002996:                                                                                                  #  02       BOFSET                 SET A SWITCH AND DOA GOTO IF IT WAS OFF
049539,002997:                                                                                                  #  03       SET                    SET A SWITCH.
049540,002998: 
049541,002999:                                                                                                  #  04       BONINV                 INVERT A SWITCH AND BRANCH IF IT WAS ON.
049542,003000:                                                                                                  #  05       INVGO                  INVERT A SWITCH AND DO A GOTO.
049543,003001:                                                                                                  #  06       BOFINV                 INVERT A SWITCH AND BRANCH IF IT WAS OFF
049544,003002:                                                                                                  #  07       INVERT                 INVERT A SWITCH.
049545,003003: 
049546,003004:                                                                                                  #  10       BONCLR                 CLEAR A SWITCH AND BRANCH IF IT WAS ON.
049547,003005:                                                                                                  #  11       CLRGO                  CLEAR A SWITCH AND DO A GOTO.
049548,003006:                                                                                                  #  12       BOFCLR                 CLEAR A SWITCH AND BRANCH IF IT WAS OFF.
049549,003007:                                                                                                  #  13       CLEAR                  CLEAR A SWITCH.
049550,003008: 
049551,003009:                                                                                                  #  14       BON                    BRANCH IF A SWITCH WAS ON.
049552,003010:                                                                                                  #  16       BOFF                   BRANCH IF A SWITCH WAS OFF.
049553,003011: 
049554,003012: 
049555,003013:                                                                                                  #           THE ADDRESS SUPPLIED WITH THE SWITCH INSTRUCTION IS INTERPRETED AS FOLLOWS:
049556,003014: 
049557,003015:                                                                                                  #           BITS 1-4    SWITCH BIT NUMBER (1-15).
049558,003016:                                                                                                  #           BITS 5-8    SWITCH OPERATION NUMBER.
049559,003017:                                                                                                  #           BITS 9-     SWITCH WORD NUMBER (UP TO 64 SWITCH WORDS).
049560,003018: 
049561,003019:                                                                                                  #           THE ADDRESS ITSELF IS MADE UP BY THE YUL SYSTEM ASSEMBLER. THE BRANCH INSTRUCTIONS REQUIRE TWO
049562,003020:                                                                                                  #  ADDRESSES, THE SECOND TAKEN AS THE DIRECT (OR INDIRECT IF IN ERASABLE) ADDRESS OF THE BRANCH.
049563,003021: 
049564,003022: 
049565,003023: 01,2543           34721        SWITCHES           CAF      LOW4                                  #  LEAVE THE SWITCH BIT IN  SWBIT  .
049566,003024: 01,2544           70117                           MASK     POLISH                                
049567,003025: 01,2545           50000                           INDEX    A                                     
049568,003026: 01,2546           34674                           CAF      BIT15                                 #  (NUMBER FROM LEFT TO RIGHT.)
049569,003027: 01,2547           54131                           TS       SWBIT                                 
049570,003028: 
049571,003029: 01,2550           34704                           CAF      BIT7                                  #  LEAVE THE SWITCH NUMBER IN SWWORD.
049572,003030: 01,2551           00006                           EXTEND                                         
049573,003031: 01,2552           70117                           MP       POLISH                                
049574,003032: 01,2553           54130                           TS       SWWORD                                
049575,003033: 
049576,003034: 01,2554           00004                           INHINT                                         #  DURING SWITCH CHANGE SO RUPT CAN USE TOO
049577,003035: 01,2555           50000                           INDEX    A                                     #  LEAVE THE SWITCH WORD ITSELF IN L.
049578,003036: 01,2556           30074                           CA       STATE                                 
049579,003037: 01,2557           54002                           TS       Q                                     #  Q WILL BE USED AS A CHANNEL.
049580,003038: 

Page 1165

049582,003040: 01,2560           34700                           CAF      BIT11                                 
049583,003041: 01,2561           00006                           EXTEND                                         #  DISPATCH SWITCH BIT OPERATION AS IN BITS
049584,003042: 01,2562           70117                           MP       POLISH                                #  7-8 OF POLISH.
049585,003043: 01,2563           72623                           MASK     B3TOB4                                #  GETS 4X2-BIT CODE.
049586,003044: 01,2564           50000                           INDEX    A                                     
049587,003045: 01,2565           12566                           TCF      +1                                    
049588,003046: 
049589,003047: 01,2566           30131                 +1        CA       SWBIT                                 #  00 - SET SWITCH IN QUESTION.
049590,003048: 01,2567           00006                           EXTEND                                         
049591,003049: 01,2570           04002                           ROR      QCHAN                                 
049592,003050: 01,2571           12600                           TCF      SWSTORE                               
049593,003051: 
049594,003052: 01,2572           30131                 +5        CA       SWBIT                                 #  01 - INVERT SWITCH.
049595,003053: 01,2573           00006                           EXTEND                                         
049596,003054: 01,2574           06002                           RXOR     QCHAN                                 
049597,003055: 01,2575           12600                           TCF      SWSTORE                               
049598,003056: 
049599,003057: 01,2576           40131                 +9D       CS       SWBIT                                 #  10 - CLEAR.
049600,003058: 01,2577           70002                           MASK     Q                                     
049601,003059: 01,2600           50130        SWSTORE            INDEX    SWWORD                                
049602,003060: 01,2601           54074                           TS       STATE                                 #  NEW SWITCH WORD.
049603,003061: 

Page 1166

049605,003063: 01,2602           00003                 +13D      RELINT                                         #  11 - NOOP.
049606,003064: 01,2603           34676                           CAF      BIT13                                 
049607,003065: 01,2604           00006                           EXTEND                                         #  DISPATCH SEQUCE CHANGING OR BRANCHING
049608,003066: 01,2605           70117                           MP       POLISH                                #  CODE.
049609,003067: 01,2606           72623                           MASK     B3TOB4                                
049610,003068: 01,2607           50000                           INDEX    A                                     
049611,003069: 01,2610           12611                           TCF      +1                                    #  ORIGINALLY STORED IN BITS 5-6.
049612,003070: 
049613,003071: 01,2611           40002                 +1        CS       Q                                     #  00 - BRANCH IF ON.
049614,003072: 01,2612           70131        TEST               MASK     SWBIT                                 
049615,003073: 01,2613           10000                           CCS      A                                     
049616,003074: 01,2614           12624                           TCF      SWSKIP                                
049617,003075: 
049618,003076: 01,2615           16664                 +5        TCF      SWBRANCH                              #  01 - GO TO.
049619,003077: 
049620,003078: 01,2616           12624                           TCF      SWSKIP                                #  HERE ONLY ON BIT 15.
049621,003079: 
049622,003080: 01,2617           05642                           TC       CCSHOLE                               
049623,003081: 01,2620           05642                           TC       CCSHOLE                               
049624,003082: 
049625,003083: 01,2621           30002                 +9D       CA       Q                                     #  10 - BRANCH IF OFF.
049626,003084: 01,2622           12612                           TCF      TEST                                  
049627,003085: 
049628,003086: 01,2623           00014        B3TOB4             OCT      0014                                  
049629,003087: 01,2624           24164        SWSKIP             INCR     LOC                                   
049630,003088: 
049631,003089: 01,2625  01,2543               SW/                EQUALS   SWITCHES                              
049632,003090: 
049633,003091: 01,2625           16030                 +13D      TCF      DANZIG                                #  11 - NOOP.

End of include-file INTERPRETER.agc.  Parent file is MAIN.agc